{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":43296,"title":"Refresh your system of equations","description":"Given square matrix, and solution vector, find the values of the variables\r\n\r\nExample:\r\n\r\nxyz = [1 -1 2; 0 2 5; 4 0 -3]; //x-y+2z; 2y+5x; 4x-3z\r\nabc = [21; 21; 21]\r\ny_correct =  [ 9 -2 5 ];","description_html":"\u003cp\u003eGiven square matrix, and solution vector, find the values of the variables\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003exyz = [1 -1 2; 0 2 5; 4 0 -3]; //x-y+2z; 2y+5x; 4x-3z\r\nabc = [21; 21; 21]\r\ny_correct =  [ 9 -2 5 ];\u003c/p\u003e","function_template":"function y = answerMe(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nxyz = [1 -1 2; 0 2 5; 4 0 -3];\r\nabc = [21; 21; 21];\r\ny_correct =  [ 9 -2 5 ];\r\nassert(sum((transpose(answerMe(xyz,abc))-y_correct))\u003c0.01)\r\n%%\r\nxyz = [1 2; 1 -2];\r\nabc = [3; -1];\r\ny_correct =  [ 1 1];\r\nassert(isequal(nnz(answerMe(xyz,abc)-y_correct),0))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":3,"created_by":13865,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":53,"test_suite_updated_at":"2016-10-29T16:24:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-10T07:22:44.000Z","updated_at":"2026-02-12T11:59:59.000Z","published_at":"2016-10-10T07:22:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven square matrix, and solution vector, find the values of the variables\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003exyz = [1 -1 2; 0 2 5; 4 0 -3]; //x-y+2z; 2y+5x; 4x-3z abc = [21; 21; 21] y_correct = [ 9 -2 5 ];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2971,"title":"square a vector-Given the variable x as your input, square it and put the result in y.","description":"function y = (x)squared\r\n \r\n y = x;\r\nend","description_html":"\u003cp\u003efunction y = (x)squared\u003c/p\u003e\u003cpre\u003e y = x;\r\nend\u003c/pre\u003e","function_template":"function y = (x)squared\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal((x)^2,y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":33779,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":112,"test_suite_updated_at":"2015-02-07T00:41:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-02-07T00:34:32.000Z","updated_at":"2026-02-19T14:25:21.000Z","published_at":"2015-02-07T00:36:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efunction y = (x)squared\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = x;\\nend]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45430,"title":"Juego de posiciones","description":"Crea una función que ordene vectores de tal manera que los primeros números sean negativos ordenados de menor a mayor. Y después vayan los números positivos ordenados de mayor a menor. \r\n\r\nPor ejemplo:\r\n\r\ny = [-1 6 15 -7 31 2 -4 -5];\r\n\r\ny_correct = [-7 -5 -4 -1 31 15 6 2];\r\n\r\nPD: Considerad el cero como número positivo. ","description_html":"\u003cp\u003eCrea una función que ordene vectores de tal manera que los primeros números sean negativos ordenados de menor a mayor. Y después vayan los números positivos ordenados de mayor a menor.\u003c/p\u003e\u003cp\u003ePor ejemplo:\u003c/p\u003e\u003cp\u003ey = [-1 6 15 -7 31 2 -4 -5];\u003c/p\u003e\u003cp\u003ey_correct = [-7 -5 -4 -1 31 15 6 2];\u003c/p\u003e\u003cp\u003ePD: Considerad el cero como número positivo.\u003c/p\u003e","function_template":"function x = order(y)\r\n \r\nend","test_suite":"%%\r\ny = [-1 6 15 -7 31 2 -4 -5];\r\ny_correct = [-7 -5 -4 -1 31 15 6 2];\r\nassert(isequal(order(y),y_correct))\r\n%%\r\ny=[6 7 -34 9 0];\r\ny_correct= [-34 9 7 6 0];\r\nassert(isequal(order(y),y_correct))\r\n%%\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":394942,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-09T11:48:17.000Z","updated_at":"2026-03-02T14:14:33.000Z","published_at":"2020-04-10T07:53:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCrea una función que ordene vectores de tal manera que los primeros números sean negativos ordenados de menor a mayor. Y después vayan los números positivos ordenados de mayor a menor.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePor ejemplo:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = [-1 6 15 -7 31 2 -4 -5];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_correct = [-7 -5 -4 -1 31 15 6 2];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePD: Considerad el cero como número positivo.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42986,"title":"Determine the roots of a cubic equation","description":"Given the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.","description_html":"\u003cp\u003eGiven the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.\u003c/p\u003e","function_template":"function y = cubicRoots(a,b,c,d)\r\n  y = [0 0 0];\r\nend","test_suite":"%%\r\na=1; b=3; c=3; d=1;\r\ny_correct = [-1 -1 -1];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)\r\n\r\n%%\r\na=1; b=-6; c=11; d=-6;\r\ny_correct = [1 2 3];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)\r\n\r\n%%\r\na=4; b=4; c=-1; d=-1;\r\ny_correct = [-1 -0.5 0.5];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":91311,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":"2016-09-30T16:42:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-09-16T10:40:42.000Z","updated_at":"2026-03-11T08:50:39.000Z","published_at":"2016-09-16T10:40:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60982,"title":"Mesh the square with triangles","description":"Problem statement\r\n\r\nAn square is a regular polygon with 4 vertices and 4 edges.\r\nA triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh, that is to say give one triangulation T of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\r\n\r\nExample\r\nThe first triangle here can be [1, 2, 3] if counterclockwise oriented.\r\n\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 995.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 497.617px; transform-origin: 408px 497.617px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.608px 8px; transform-origin: 183.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.983px 8px; transform-origin: 176.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.633px 8px; transform-origin: 132.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.275px 8px; transform-origin: 192.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh, that is to say give one triangulation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.583px 8px; transform-origin: 183.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.8583px 8px; transform-origin: 89.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 340.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 170.25px; text-align: left; transform-origin: 385px 170.25px; 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margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_square()\r\n  T = 1;\r\nend","test_suite":"%% Test every possible solutions\r\nT_correct1 = [1 2 3;\r\n              3 4 1];\r\n\r\nT_correct2 = [2 3 4;\r\n              1 2 4];\r\n\r\nassert(isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct1,2)))...\r\n     | isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct2,2))))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_square.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:45:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T16:29:27.000Z","updated_at":"2026-02-10T17:10:21.000Z","published_at":"2025-07-23T16:40:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh, that is to say give one triangulation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"335\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"447\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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Are you more familiar with iteration methods or Linear Algebra ? Let's see together.","description":"Referring to problem:\r\n\r\nhttps://www.mathworks.com/matlabcentral/cody/problems/44530-are-you-more-familiar-with-iteration-methods-or-linear-algebra-let-s-see-together\r\n\r\nGiven a sum result *_x_* value of a *_N_* number of addends, build an array of _*N*_ elements _*y*_ such that the following equality is satisfied: _sum(y) = x_ .\r\n\r\nFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].\r\n\r\nMore formally if x = a and N = n it results: \r\n\r\ny = [y_1 y_2 y_3 ... y_n]\r\nwhere:  y_1 + y_2 + y_3 +...+ y_n = a\r\n\r\nImportant notice: All the elements in y must be: *different from zero*, *different from each other* and *strictly positive* . On the other hand I will not take into account if they are _integers or decimal numbers_ .\r\n\r\nHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\r\n\r\nGood luck and enjoy with the solution ;)","description_html":"\u003cp\u003eReferring to problem:\u003c/p\u003e\u003cp\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/44530-are-you-more-familiar-with-iteration-methods-or-linear-algebra-let-s-see-together\u003c/p\u003e\u003cp\u003eGiven a sum result \u003cb\u003e\u003ci\u003ex\u003c/i\u003e\u003c/b\u003e value of a \u003cb\u003e\u003ci\u003eN\u003c/i\u003e\u003c/b\u003e number of addends, build an array of \u003ci\u003e\u003cb\u003eN\u003c/b\u003e\u003c/i\u003e elements \u003ci\u003e\u003cb\u003ey\u003c/b\u003e\u003c/i\u003e such that the following equality is satisfied: \u003ci\u003esum(y) = x\u003c/i\u003e .\u003c/p\u003e\u003cp\u003eFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].\u003c/p\u003e\u003cp\u003eMore formally if x = a and N = n it results:\u003c/p\u003e\u003cp\u003ey = [y_1 y_2 y_3 ... y_n]\r\nwhere:  y_1 + y_2 + y_3 +...+ y_n = a\u003c/p\u003e\u003cp\u003eImportant notice: All the elements in y must be: \u003cb\u003edifferent from zero\u003c/b\u003e, \u003cb\u003edifferent from each other\u003c/b\u003e and \u003cb\u003estrictly positive\u003c/b\u003e . On the other hand I will not take into account if they are \u003ci\u003eintegers or decimal numbers\u003c/i\u003e .\u003c/p\u003e\u003cp\u003eHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\u003c/p\u003e\u003cp\u003eGood luck and enjoy with the solution ;)\u003c/p\u003e","function_template":"function y = buildSumArray(x,N);\r\n  y = sum(1:N);\r\nend","test_suite":"%% Test Case 1\r\nx = 6;\r\nN = 3;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\nassert(isempty(y(y \u003c 0)))\r\n\r\n%% Test Case 2\r\nx = 13;\r\nN = 5;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\nassert(isempty(y(y \u003c 0)))\r\n\r\n%% Test Case 3\r\nx = 78;\r\nN = 11;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\nassert(isempty(y(y \u003c 0)))\r\n\r\n%% Test Case 4\r\nx = 2689;\r\nN = 245;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\nassert(isempty(y(y \u003c 0)))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":181340,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":677,"created_at":"2018-02-24T14:17:32.000Z","updated_at":"2026-03-05T10:42:37.000Z","published_at":"2018-02-24T14:18:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReferring to problem:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44530-are-you-more-familiar-with-iteration-methods-or-linear-algebra-let-s-see-together\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/44530-are-you-more-familiar-with-iteration-methods-or-linear-algebra-let-s-see-together\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a sum result\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e value of a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number of addends, build an array of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e elements\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that the following equality is satisfied:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum(y) = x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or [8 2].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore formally if x = a and N = n it results:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = [y_1 y_2 y_3 ... y_n] where: y_1 + y_2 + y_3 +...+ y_n = a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImportant notice: All the elements in y must be:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edifferent from zero\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edifferent from each other\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estrictly positive\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . On the other hand I will not take into account if they are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegers or decimal numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck and enjoy with the solution ;)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60306,"title":"Add non-triangular numbers","description":"The nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems 5, 291, 44289, 44334, 44732, 55680, 55695, 55705, 55710, and 55715, for example. \r\nWrite a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.658px 8px; transform-origin: 377.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/5\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e5\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/291\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e291\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44289\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44289\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44334\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44334\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44732\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44732\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55680\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55680\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55695\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55695\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55705\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55705\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55710\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55710\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.775px 8px; transform-origin: 16.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55715\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55715\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, for example. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 362.975px 8px; transform-origin: 362.975px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = addNonTriangular(n)\r\n  y = sum(tril(n)+1:triu(n)-1);\r\nend","test_suite":"%%\r\nassert(isequal(addNonTriangular(1),2))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(2),9))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(3),24))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(4),50))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(44),44550))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(92),397854))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(267),9588504))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(389),29583450))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(461),49198842))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(556),86249222))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(632),126617724))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(709),178703450))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(878),339189399))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(913),381358274))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(1255),989903840))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(6534),139521237075))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(14342),1475229944979))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(78422),241154195453019))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(256347),8422831459859544))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(addNonTriangular(2429)/(3^10*347)),21560175))\r\n\r\n%%\r\ns = [0 1 4 9 6 5 6 9 4 1];\r\nn = randi(1000);\r\nm = n:n+2;\r\nd = num2str((2*arrayfun(@addNonTriangular,m)./m)')-'0';\r\nd1 = d(:,end)';\r\nassert(~isempty(strfind([s s],d1)))\r\n\r\n%%\r\nfiletext = fileread('addNonTriangular.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'sum') || contains(filetext,'trace')  || contains(filetext,'ones')  || contains(filetext,'eye'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-14T01:38:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-14T01:37:57.000Z","updated_at":"2026-03-04T14:14:54.000Z","published_at":"2024-05-14T01:38:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/5\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/291\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e291\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44289\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44289\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44334\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44334\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44732\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44732\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55680\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55680\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55695\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55695\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55705\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55705\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55710\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55710\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55715\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55715\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, for example. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60980,"title":"Mesh the tetrahedron","description":"Problem statement\r\n\r\nAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\r\nA triangulated mesh -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, T. You will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles [1, 2, 3] and [3, 2, 1] are distinct).\r\nOn the other hand [1, 2, 3], [2, 3, 1] and [3, 1, 2] are one same unique triangle.\r\nThe row order of the triangles in the list doesn't matter.\r\n       \r\nEdit / update\r\nTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\r\n\r\nExample\r\nThe first triangle (X \u003e 0 and Y \u003e 0) here can be [1, 2, 4] if counterclockwise oriented (normals outward).\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1194.73px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 597.367px; transform-origin: 408px 597.367px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.592px 8px; transform-origin: 374.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.542px 8px; transform-origin: 157.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.533px 8px; transform-origin: 206.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 328.017px 8px; transform-origin: 328.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.51667px 8px; transform-origin: 7.51667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.4667px 8px; transform-origin: 49.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 2, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.0583px 8px; transform-origin: 40.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are distinct).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the other hand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[2, 3, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 1, 2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5333px 8px; transform-origin: 94.5333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are one same unique triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.5917px 8px; transform-origin: 13.5917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e       \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.9833px 8px; transform-origin: 41.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdit / update\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 351.75px 8px; transform-origin: 351.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.1167px 8px; transform-origin: 52.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.2917px 8px; transform-origin: 53.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(X \u0026gt; 0 and Y \u0026gt; 0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 4]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148.208px 8px; transform-origin: 148.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented (normals outward).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_tetrahedron()\r\n  T = 1;\r\nend","test_suite":"%%\r\nT_correct = [1 2 4;\r\n             2 3 4;\r\n             3 1 4;\r\n             1 3 2];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_tetrahedron(),2)),sortrows(sort(T_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_tetrahedron.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:43:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":"2025-07-23T16:17:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T11:03:01.000Z","updated_at":"2026-03-31T18:44:34.000Z","published_at":"2025-07-23T11:11:01.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are distinct).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[2, 3, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are one same unique triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEdit / update\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(X \u0026gt; 0 and Y \u0026gt; 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented (normals outward).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"378\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"504\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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gfPqz/fik4ZAFoj4ACAmMaBeer2jRxm7Lrm/O5MDpzM1RO8fr5f8M53DkcVXQQAaIGAAwAy0M/YW03U5+fDwYavIYLuTE6dzPFrLuMAgBIJOAAgmnE8PrV948iMnVT/GjZ/GeF0ZyKZAIDWCDgAYCN1ZQqZCBVt2MQBAMURcABAHONgfGD7RibRxm43HFQhVLRxgIwDAEog4ACAVPpcw7QcWqRoY7+JAwAogYADACIYU4xh+4ZcI45I0cYlb1QBgIIIOAAgJtFGNC4rAHCVgAMAQhsTjee97W39AWF11zdZumETBwCUQsABABQjZbRxScYBAEUQcABAUMVt3zg7Gw7ytkm0AQAURMABAGQth2jDJg4AyJ+AAwDC8dM3gsoh2jhAxgEAWRJwAEAgZaUbu91wkKUMo439Jg4AIEsCDgAgIxlGG5e8UQUAcibgAIAQvDlltZyjDQAgfwIOAGBjBUUbNnEAQLYEHACwmu0bSxUUbVyScQBAngQcAMA2xAMAQEACDgBYp+jtG2dnw0FaJW7cuMomDgDIkIADAEin9GjjABkHAORBwAEAK/jpG5NVFm3sN3EAAHkQcABAe3a74SCJyqKNS96oAgBZEXAAwFK2b9yl1mjjABkHAGxNwAEAhNdItOGNKgCQDwEHACxi+8YRjUQbl7xRBQAyIeAAAMJoLdoAALIi4ACA+WzfuK7paOPi4gv+6l+9PB4OAIDkBBwA0Kqzs+FghXajjYuL4dc9Mg4A2JyAAwBmGidY2zeajjYAgMwIOACA2br5vsUR/2S0YRMHAGxLwAEAc4yza8HbN3a74WAR0cYkMg4ASE7AAQCTtT21thht9LnG5LrvN3EAAMkJOABgttZ++ka70cZ83qgCAFsRcADANOO82lS6IdoAAEoh4AAADhBtLGYTBwBsQsABABOMk2oL2zdEG+vJOAAgPQEHADTp7Gw4uKK5aKPPNWQQAFAFAQcA3GUcgCvevtFotBGTTRwAkJiAAwBaJ9qITsYBAPEJOADgpHE0rWT7xm43HNzTnVtDk3fyaGO/iQMAiE/AAQAtaija6HONtNHGJW9UAYBkBBwAcNw4lNb00zeaizYAgDYIOACgFaKNTdjEAQBpCDgA4IhxHK1g+4ZoY1syDgBIQMABADVrJdrocw3xAQA0TMABAIeMo3K52zdORRtnZ8NBBQrJNWziAIDYBBwAUJtT0UZ97rsv1q94ZBwAEIGAAwBuKXb7xqRow3R9Wnd9+l+h7TdxAAARCDgAoAaToo03v1m6cVS0XOMqb1QBgHgEHABw3Th5FrR9w6y8XJJcAwBIQMABAAXr5nKj+UIb5Ro2cQBAJAIOALhinDnz374h2liozzU2DRdkHAAQg4ADAEaFpBuijSUyyDUAgKgEHABQDNHGbLnmGjZxAEBwAg4AuGecM/PcvhEy2jg/Hw4qlmuucZiMAwBCEHAAQNZCRhvVKyrX2G/iAABCEHAAwP7/Qs9q+4ZoY6qico2rvFEFAAIScABAdqJEG29+83BQjWJzDQAgBgEHAM0bJ+Qctm9EiTY6laUAFeUaNnEAQCgCDgDIQsRoo5rJuT+X6oIAGQcABCHgAKBt40i57faN8HNtTVlATecCAEQj4ACALXVTe+DBXa5RIJs4AGA9AQcADRuHyU22b3RfO/AsW0cc0J9FBSeyWMvnDgArCDgAILUto43z8+EgN/0pNDzb7zdxAACLCDgAaNU4S6fcvhE42qggFKjgFMLxRhUAWEPAAQApRIk2ytW/fmM8ABCOgAOAJo2jdYLtG1lEG7vdcLCt/sUveP3NsIkDABYTcABALFlEG5mQa0wm4wCAZQQcALRnnBvjbd/ovkCw2bSPBgqddYt+8QBAUQQcABBS+GijRHKNdWziAIAFBBwANGacGGNs32g92uhfdomvPGeuJwBMI+AAgAC6GTTMGFpiQNC/ZnN4UPtNHADANAIOAFoyDuEBt2+EiTbSZATn58NBEGlec8O8UQUAZhFwANCMcUoMlW50ny7A3FlcRtC/4LJeMwDQAAEHAMzWYrQh19iCTRwAMJ2AA4A2jPPhyu0b3WcJMGgmTgp2u+Fggf6lpny1XCfjAICJBBwAMEmR0cYacg0AoCgCDgAaMA7qy7ZvBIg2+rCgiLygoJfaDJs4AGAKAQcAHBUs2shf/zrNz/lTIwA4QsABQO3GgXDW9o3uv1k7RxaRF/QvMv/X2bz9Jg4A4AgBBwBc00S0Idco0CPeqAIAJwk4AKjaOApO3L6xanDMPDU4P8/9FXJEV7CbNVNEALhFwAEAzzowQ05XRGpgJC7QjbZ85Id/eDgCAG4RcABQr3GkP71948YMOU8R0QYFutaWfZvd67R9xqHxAOA6AQcA7bo2Q841Dpy52+2GAwpxrS1LaTMAyICAA4BKjWPhwe0b12bIWfqB08xJBNfa8nib2cQBAAcJOABoy7UZcha5BtFca8sJnSbjAIDbBBwA1Gic+q5u37g2Q84yYeCExfa9pdMAYAUBBwD1E22Qp+WdaRMHANwi4ACgOuO897y3vW3hANnnGuZGolnYmcfoVQAQcABQseXRRn3OzoYDthYw2thv4gAABBwA1GaMJ77g0F+eckqt0QbZCBhtXPJGFQC4JOAAoHmiDSKLEW0AADcIOACoyJhTTN2+UX20sdsNB2wkQbRhEwcA9AQcANRierrR5xqmQWJKEG1cknEAQEfAAUBL5BrElzLaAAAuCTgAqMIYWxzdviHaIL4Now2bOABAwAFA7UQbxLdhtHGAhgegSQIOAMo3jnPXtm/0uYZJj/gyabL9Jg4AaJKAA4DqyDVuODsbDgit67OsWs0bVQBomYADgMKNg9yz2zdEG6QSMtro+1brAsA6Ag4AamE+JIlg0UacXMMmDgCaJeAAoGTjCPcFP/RD/QF7u91wQCBhoo04ucZVMg4A2iTgAAC4Q4BoI36uAQCNE3AAUKxxVrR9g3jWRhsb5Ro2cQDQIAEHAMABq6KNjXKNw2QcALRBwAFAmcaZzfYNggsQbWRgv4kDANog4AAAGCyPNvpcI49o45I3qgDQFAEHAAUapzXbN+52djYccNLCaCPLXAMA2iTgAABaNzufKCfXsIkDgHYIOAAozTin2b7Bel0zzZj7y8k1rpJxANAIAQcA1Gi3Gw44Yka0UWauAQCtEXAAUJRxyLR9g8WmRhsV5Ro2cQDQAgEHAOUwm7HOpGijolzjMPcRAJUScABQHts3mOvuaKP2XGO/iQMAKiXgAKAQ4+Qp3WCWqdFGA7xRBYC6CTgAgDrdEW30uYZRHwBqIeAAoATjFGr7xjxnZ8NBY05FG23nGjZxAFAxAQcAUI+j0UbbucZVMg4AaiXgACB74xhm+wanHZjX5RoA0AwBBwBUZ7cbDppxcSPdkGucZBMHAFUScACQt3EAs32Dg65FG3KNBVwuAGoh4AAAirSPNuQa8+03cQBALQQcAGRsHFlt31ii3oH/ZrTBIt6oAkBlBBwAUJ16x/4h2uhP0FgOAFwh4AAgV+P4avsGnWejDblGaDZxAFATAQcAVOr8fDgo3MU9JvBIZBwAVEPAAUCWxlnL9o129cGGqRsAmEbAAQDk5N5mDcFGSjZxAFAHAQcA+bF9Y403v3k4KMu9XOPZaKM7HD7EFmQcABRLwAEAbGfMNYbf9f8guf0mDgAoloADgMyMs67tGzW7nmt0uiPpxra8UQWA0gk4AICErucaHdEGABCEgAOAnIyjr+0btelzDdFG3mziAKBoAg4AsiHdWOlWgrC9/iXdelXd7w3QeZJxAFAuAQcAlO92iHB+Phxson89hyZk0QYAEImAA4A8jMOw7RvzHMkRttG/mCOvR7RRCps4ACiUgAMACnQySkjtrhcj2ihYJj0GABMIOADIwDhE2b5xt5NRwnN2u+Eggf6VnHgx93IN83GJ9ps4AKAcAg4AKMRdaUIiE3KNjmijVGN9H/krf2X/EQAogYADgK2N45PtG0f1M+fmpr2M7k8YiIt0or45tB8A3EXAAQC56gfOzWfLOS/DHFykI/Xdb+IAgBIIOADY1DhW2b5xzeRAIaL+NUx+Gd2f2/oVM99dJfZGFQAKIuAAgJzMyRSi6F/AnNfQ/VGzb2HmVxkA8ifgAGA743xl+8azAg6c5+fDwXT9V5/5Aro/bUQuzPwq28QBQCkEHACwqX7g3Gp0XPrVu//AsFuYIG22/jMAQDQCDgA2Mk5K7W7fCDJwLtN/6UVfvftvzLiFWd1pftooAEUQcABAcqsHzsN2u+HgmP7rLv3Soo3CrCv3Dd6oAkD+BBwAbGGckZrbvhFu4Jyh/6Irvm73XxpqSxK7zaJ+cgBYSsABAPH1A2f6sXD1F+3+Y7NsSWK2mTeqAJA5AQcAyY0DWBPbN2IOnEf1X3Td1+3+4+SvmxWSdJo3qgCQMwEHAMSRZOCMQbRRkr7NxA0AIOAAILVxEqt5+0bJA6dBuRgbtZlNHABkS8ABAOHkEG2cnQ0HM3Wv28Bahq3bTMYBQJ4EHAAkNI5DtW3f6AfOYoe97nWbU8tQcpsBQGwCDgBSGQezqtKNwgdO0UYxMus0mzgAyJCAAwAWyS3a2O2Gg2lEG2Xo2yzzECHzlwdAMwQcACQxjkA1bN/If+A8qXvp5tECZN9m+00cAJAHAQcATNMPnKINYiunzbxRBYCsCDgAiG8cfkrdvlHOwHlM9+oNoAUov9MAYEMCDgA4TrQBJ9nEAUA+BBwARDaOPYVt3xBtwDQyDgAyIeAAgCv6XKP8Oc2gCQC0RsABQExjUlDA9o0qco3nnJ115yDdIDGbOADIgYADgObVEW3cyzUMl2xPxgHARgQcAEQzzjn5bt+oJtrY7cyUbGu/iQMANiLgAKBJ1UQb935Rtr4by29Ib1QBYFsCDgDiGCecvLZv1DJJdrpzMESWraJuBIAcCDgAyEPsSa+iSVK0Uba+FWvpxkt9W36+TRwAbEfAAUAE42wzaftG7GEv9udPqDsNU2Op+j6spRVvuHpWMg4AtiLgAGAjCea92J8/oe40DItFStDnm9KZAORDwAFAaOMsd3T7Rux5r//8Ub9EQgbIUlXUhAed6EybOADYhIADgIRij3x1jZQnBsjDzs6GAzbUN2FFfXjbvM6s+lIAkBUBBwBBjcPMze0bsUe+2J8/OUNhYfoOrKsJb+tOb+IZ7jdxAEAqAg4Awjk43c2a+vo/vOBXRabPkIPdbjggnhv9dvtX7Wa3pTeqAJCcgAOA8J7dvtHM4BfQghmS6JpvY20JQCkEHAAEMg6BX/CDPyjXmMsMmSPRxuq2tIkDgJQEHACwpfUzJIH1uYZoYzhcS8YBQDICDgBCGEeXZ7dvME3AGZIwms81OtoSgHIJOAAgNTNkdkQb90S6BDZxAJCGgAOA1cahxfaNO3VXyoSXF9HGPek609UGIBoBBwCkEH2APDsbDpiizzUM2wk68579Jg4AiEbAAcA644ho+8YxaQZIppJrjBJ3pjeqABCbgAMAYkk8QHIH0cZIZwJQJQEHACuM46LtG7clGiB3u+GAE0Qbo22jDZs4AIhKwAEAgW07Q7LX5xpm6XsyaUsZBwDxCDgAWGqcT2zfuJTJDIlc4yptCUAjBBwAEIAZMheijSvybEubOACIRMABwCLjZGL7Rp4zZHP6XMPAPCqmLZUMgHAEHACwUDEzZMXkGrcU0Zb7TRwAEI6AA4D5xnmy2e0b2c2QZ2fDQSPkGkcUdEW8UQWA4AQcADBDdtFGU+Qax+lMABBwADDTOF62tn3DALkZucZJ5XamTRwAhCXgAIA75DtA7nbDQZXkGnfJtzMnk3EAEJCAA4A5xiGkne0bpq7U5BoTdFfHBQKAGwQcAEzWWLphhkxKrjFNVW15r+Kf/4537H8LACsIOADgpqpmyMzJNSarqi2PFV0nALCCgAOAacbBo+7tG1XNkJk7NuJyS1Vteaju+00cALCCgAMAnlXVDJmzfr4VbUxTVVuerLs3qgCwnoADgAnGkaPK7Rtlz5Bdac7OhuOc9cOt2XWystvyqgWl1ycALCLgAKBdxc+Q+c+BC4bb5hXflpdmlt4bVQBYScABwF3GEaWm7Rv1zJB56ifbOcMtvUou2dLqe6MKAGsIOABoSzc2VTI5vfnNw0E++rHWaLpIJZ2pAQDYjoADgJPGWaWC7RuVDJAZ6mdaY+1SNXRmuB6wiQOAxQQcANSvhgEyQ+Fm2mbV0JlRe0B3ATCHgAOA48bpoujtGyak8KLOtG3oLl/xVzBaG/hpowAsI+AAoFo1zJBZ6Qda0cY6NbRl/DbwRhUAFhBwAHDEOFeUuH2jhhkyH/00a85crfi23KoT9B4A0wg4AKhK8TPkXOfnw0FwW02zNSq+LbfoBG9UAWAuAQcAh4zDTEHbN4qfITPRj7LJp9laFd+WmzaDN6oAMIuAA4DiFT9DztIPnMHnvUiftmHFt6V+AKA0Ag4Abhmnmvy3b+Q1Q8aeBq8OnLvdcLBS/zljv/L2FHxBM2sJmzgAmE7AAUCRulkno3En9kAY/PP3nzDqa25VXp05S64tIeMAYCIBBwDXjSNEtts3Mhog+4Ew6tAV9vMneMENy6gz59IVAFRBwAFAMTIaIGMPhP3nD/glYr/gtmXUmXMV0hg2cQAwhYADgCvG4SG37RsZDZCxB8Kwn7//bFFfcNsy6sy5ym0M/QzAEQIOAEbj2JBhupGF2ANhwM/ff6qor7Z53cUt8voW2xv7TRwAcISAA4B85TJDxh4IF3/+8/PhoNd/nqgvlXzacq7ye8MbVQA4TcABwD3jwJDJ9o0sZsh+IIw3SoX6/KE+D3fJoi0X0B4AtEHAAUBespghYw+EoT5/7NfJKIu2XKC6DrGJA4ATBBwA7EeFbbdvZDFDxh4Ig3z+3W44IL4s2nKuvs2idvJ2ZBwAHCPgAGB7WcyQsQfCegfOWmXRlnNpMwAaJuAAaN44Dm2yfWP7GbIfCOPNhLE/P3GUV7CW2swmDgAOEnAAsI1uLtl4NIk9ELY0cNZk+86cq/FOc5cBMBJwALRtnA1Sbt/YfoCMPRDG/vzEsX1nztK3Waudtt/EAQAjAQcA6Ww/QMYeCBseOIu2fWfOos3u8UYVAG4QcAA0bJwK0mzf2HIE6QfCyqags7PhgBW6niipLeprYwAIR8ABQHRbzpAGQo7Ysi0X0MmH2MQBwFUCDoBWjfNA1O0bW86QBkKO2LItF9DJJ8k4ALgk4AAgii1nyLoHwt1uOGC+Ldtyrr6NDe0AMJmAA6BJ49QUY/vGZjOkgZDjNmvLBbTxTDZxANATcAAQzGYzpIGQ4zZrywV08nouIEDDBBwA7RkHgIDbNzabIQ2EHLdZWy6gk9fZb+IAoGECDgBW2WyGNBByUhnN0bexTg7BG1UAEHAANGZc+q/fvtF9om3GCAMhJ23WmbNoYwAITcABwGzbDJD9QGgm7J2dDQdcsU1nzqWNo7GJA6BxAg6AloyL/sXbN7YZIA2E3GWbzpxLJ8cn4wBomYADoBnjcn9NupGagZC7dP2Re4v0bayTASAyAQcAd9tghjQQHrTbDQds0pZzaeMt2MQB0CwBB0AbxoX+3O0bqWfIfiA0lnBS6rZcQBtnQhUAWiLgAOCw1DOkgZAJUrflAjo5A/tNHAC0RMAB0IBx3Jq4fSP1DGkgZILUbTlX38Y6ORveqALQIAEHAHupZ0gDIROkbsu5tDEA5EHAAVC7cfQ6vX0j6QzZD4RmQu6StC0X0MZ5s4kDoDUCDoDWJZ0hDYRBnJ0NB1XLulF0ciFkHABNEXAAVG1c0x/cvtH9u3RLfgMhkyXtzLl0MgDkSsAB0KKkA6SBkMmSduYsfRvr5ALZxAHQDgEHQL3G1fzV7RvpBkgDYXC73XBQo3SdOZc2rolSAlRNwAHQkERLewMhc3S9kmm76ORa7DdxAFA1AQdApcbBrN++kWiGNBAyR6K2XEAnV8cbVQBaIOAAqFyiGdJAyByJ2nKuvo11MgCUScABUKNxQnvk0F+eEpiBkDmyjjao2MXF57/97ZfHwwEAdRFwALBIPxCaE5hMtME2rpRYxgFQNwEHQHXGhXus7RtXpgU2cHY2HJSja5ccO0YnV0+JARoj4ABgMtMC8yXqmOnN2f9JnVyxkyW2iQOgYgIOgLqMS/bA2zeOTwtwTNcx0Zum78yJzamNqzehxNf+tX4AqIuAA6AiwRfr/bRgBsjBbjcclKDrmLhNM7cztXH1JpT4si0fvtzEAUBdBBwAFQqwfcNAyCKXM2QUfVvO6kydXL0JJb7dlvuMQ3sAVETAAVCLcZm+Nt2YMC3AbbdnyGD6npzVlgv+E4ozocST2lKfANRCwAHAyEDIIpNmyAX6hpzbk9q4etMa48629EYVgPoIOACqMK71l2zfmDYtwG13zpBLrGlIbVy3aY0xvS29UQWgMgIOgIZNmxbgtukz5FR9N2pIDprcGxoIoGUCDoDyjev+Gds3TJKFOjsbDrbT9U3g1tGNnDC5PZZ1pk0cADURcAA0xjDJUssGyKP6VtSNHDSnPYJ1pm4EKJyAA6Bw44r8ju0bc6YFuCHYANnRipw2pz2CdKafNgpQDQEHQO0MkxXY7YaDLYTpnr4PtSInzOmQ7s8FbCZvVAGog4ADoGTjWvzw9o050wLcFmCG7JtQH3LanCYJ0JanaVeAYgk4AGpkpGSdtTNk34GakNNm9snatjzJG1UAKiDgACjWOBVc274xZ1qA21bNkH376UDuNLNPVrXlZN6oAlA6AQdAFfppwaKcFZbPkNqP6Wa2yvK2BKA9Ag6AMo0TwiM/8AMGS1ZaPkPOHFZp2sxuWd6WK9jEAVA0AQcAFOLsbDgIZ+EM2U+qJkAmmt8tG/aWjAOgXAIOgAKNy+5nt2/AIl0PzZ7e+jHV1MdEixpmSWcCwD0CDgBoy+wBctGYStMWNczszozGJg6AQgk4AEozLrht32jFbjccrDZvgOxnVAMesyzqmXmdmZhbAKAcAg4AyN7qoGHGANl/LUMdcy1qmxmdmdZ+EwcA5RBwABRlnB9s32jI6qxh0n/fT6ervxbNWdo53X+Qebd5owpAcQQcAOUYF9nSDSa6e4ZcOp3C4s65uy0BYBEBBwBU6I4ZUq7BGs1EGzZxAJRFwAFQiHF5bfsGp90xQy4dTeFZS/vnjrbMmIwDoCACDgAowfn5cHDcqRmyn0tNaCyzon9OtSUABCXgACjBOFfYvsFBR2fIFXMpPGtF/xxty9LYxAFQCgEHABTs8AzZD6WGMdZY10LVNp/bCiBjAg6A7I3rads3chdj8nnzm4eDW7ovdvPr9ROpAYyV1nXRgc4s334TBwAZE3AAwGppY4WbA2T/1RO+AOq0upFudmZdvFEFIH8CDoC8jStp2zcytW4gnOvaANl/6YRfnWqtbqRrnQkAGxFwAMB8CcKFW59/+E2CL007VvdS9x+304s2cQBkTsABkLFxDW37RkZWD4R36D//9S/R/ebZ38f+0jRldTsNbdkYGQdAzgQcADBN7Hzh0Offz5CmKUJZ3cn7tgSAnAg4AHI1TiC2b2xv9UB4h0Of/9oMeXY2HMBifZut6+RrbdkqmzgAsiXgAIAjQgyEdzj0+c2QBBaijbXlYVGfDwDMJOAAyNK4aLZ9YxshBsJT+s9/60t0vzctEVKITtaWt+03cQCQEwEHAFwRYiA85cjnPzxD7nbDAcwVopMPtyX3eKMKQIYEHAD5GZfLtm8kFWIgPOXI5+8+ZDwimL7NQnSytgSgOAIOAJoXaCA86sjn7z5khiSYcG2sMyeyiQMgNwIOgMyMC2XbN6LrB8J4k8nxz999yDxEMOHaWGfOJeMAyIqAA4D2hBsIDzv++Q2QhBSuk3UmABUQcADkZJxVbN+IJdxAeNjJz2+AJIy+zQJ1cvdZdOYaNnEA5EPAAZCNcXEs3Ygi3EC4wKoZ8uxsOICgbbyqLTlou4cMAB0BBwBV6wfC7aYOMyRhBG1jbRnWfhMHAJsScADkYRxdbN8IZtNco2OGJAzRRgm8UQUgBwIOAKpTR7Sx2w0HtKlv43CdHKYtASBjAg6ADIwzjO0bawUdCBeIMkPed9+1X1QvdBtHaUtusYkDYHMCDgDK1w+Emw4VKWbIrc+R6CKUWMekJOMA2JaAA2Br4zrY9o0lIgyEc3VfPvoryOA0iStCiVN0JgDkRMABQJkymPkTDZCijbqJNupiEwfAhgQcAJsaV8C2b8wQYSCcywDJWn0bh+5knZmXrZ9UAK0RcABQiDgD4VypB8izs+GAasRp49SdyXEPv+1twxEAaQk4ALYzDjm2b9whg1yjZ4BkFdFG9cYS7zOOPJ5dAI0QcACQsTgD4QJmSFaJ08naMiPZPKwAWibgANjIuBS2feOwbKaFbWbI3W44oGh9G0fo5G3aktuOl9gmDoD0BBwAZObItJCeGZLlorWxtszFhBLLOAASE3AAbGFc7Nq+sddPC3mMAd2LMI6wULQ21pa5yOZJBcANAg4AtpbTtGCGZLlonawtczG/xDZxAKQk4ABIblzm2r6xYFqIp3sd5g+W6Ns4WidryywEKXG0JgGgJ+AAYAsxB8K5utdh7GCJyG2sM7fXl3hdlfebOACITMABkNa4UG50+0aIaSGg3AfIs7PhgNxEbuPcO7MFQUvsjSoAaQg4AEgi8kA4lwGShSJ3ss7cXuyHVU5PQoDKCDgAEhrXtW1t34g9LcxnvGC2vo1jdnL3qXXmxmKW2BtVABIQcACkMq6bG0o3Ig+EC5QxQ+52wwE5iN/GZbRlxfoSx39YeaMKQGwCDgBCSzUtzGKGZLb4bawtN5bfkwqANQQcAEmMa+jKt29kOS2YIZktfidry41t9LCyiQMgKgEHACFsNC2cZoZktvidrC03ls/DKr9nJkDpBBwA8Y2r2Dq3b+QzLVzRvSCjAzP0bRy5k7XllpKUeAo/bRQgHgEHAItkMy3cYIZkniRtrC23lN+TyhtVACIRcABENq5f69m+kd+00OteU1WzwtnZcEAkqTq5qrYsS64Pq2vyf4UA5RBwADBZrtNC95qMCMyQqpN15mZyfVhd8kYVgBgEHAAxjSvs4rdv5DotGCCZoW/jJJ2sM7eRsMTreaMKQHACDgBOynVaqHaA3O2Gg6j6srYzViU82Wo7M3NN9TMARwg4AKIZV9tFbt/op4VcBwZzzHI3yppriYNJ2Mbdl9GZG0hY4uBs4gAIS8ABwHV5TwtmyIX6sh6sbN4VXy7heWnLbVTRujIOgIAEHABxjEvVkrZv5D0tdK/M8n+JiWXNuPTz9Oeb6nS05TYSlhiAggg4AMh9WjBDLjS3rKVPjGnbWFtuoC9x6Y16i00cAKEIOAAiGBepuW/fyH5a6F6Z9f4Si8uadz8clfZla8sNFNqZCzRymgBxCDgAmpT9tGCGXKIv6/rK5t0b1wQ538m05QbSlngr+00cAKwg4AAIbVyLZ7p9I/tpwQz5rLOz4WCi4GXNu0mG8034IrXlBtKWeHPeqAKwnoADoBnZTwtmyCXilTXPhtniVWnLpPoSZ9h7AGRPwAEQ1Lgoz2j7RgnTQvfiTDPP2u2GgynSlDWfztmijXVmUluUOCs2cQCsJOAACGdckuaSbpQwLXSvz0J+tsSV3byLtuhknZnUFiXOk4wDYA0BB0CNSpgWDJCz9WXdpLJbtdMW56szk9qqpQGokYADIJBxjb7x9o1CpgUDzTw5lDXla+i/VvJT7r6ezkxkoxIXwSYOgMUEHAC1KGRaMEPOk1tZY7+Yjc5XW6aTW0tnzrUCmEPAARDCuAbdYPtGPy2UsAjuXqKl+gzZljXSq9rofLVlOtm2dH72mzgAmEPAAVCscqYFM+RsmVc2bO9t1MnaMp2NSlyovjOf640qAPMJOABWG1ef6bZvlDMt9Ct15nnsseEgcyubsG/jLTpZWyayXYkLpTMBVhJwABSlnGnBSr0Jy7pxuzbWlomU86TKxMHOtIkDYC4BB8A647oz7vaNflooZI17cKXOHbri7nbDcVlmdeambawtU9i0xCXqLtaJ6yXjAJhFwAGQt6KmhdMrdQ6rYyC88xQ2PU2dmUIdnZyQtgQITsABsMK4mo+yfaOoacFKfYnKBsKD59Kf43anqTNT2LTEJZrVljZxAEwn4ADIT1HTwqyVOoNaB8Kr57X1OerM6PoSb1rl4qxtS1cb4CQBB8BS40Iz2PaNAqcFa+15ppS4qAY47M5zjKz72jozrq1LXKI1bbnfxAHASQIOgAwUOC2sWay3aEqJC2yD3GjL6HTpfEHa0htVAKYQcAAsMi4x127fKHBaCLJYb0iBJS6RtoxOJ8+nLQESE3AAbKTAacFifZ5lJT47Gw6YRlvG1bdxaQ+rHAS/ZDZxANxJwAEw37i4XLJ9o8xpoXu5FtQzFFjiEmnLuLTxUvE6U8YBcJqAAyCVMqeFeCv1CvUlXlbl3W44YAJtGVeZD6sc6EyAbQk4AGYa1/0ztm+UOS1Yqc9gIExFW8alk5dK1pk2cQCcIOAAiKnMaSHZSr0GBsKEXOhY+jbWyYts+cBUMoDrBBwAc4yrybu3b5Q5LWy5Ui9OmSUulM6MRRuvsFVb7jdxAHCdgANgsnEMOJVu9NNCgQPDViv18hRb4kLpzFi08Qqbt6U3qgAcJOAACKTYaWHzlXoxDIRp6cxYdPIK2hIgZwIOgGnGeeDA9o2SpwUr9UkMhGl119rlDq9vY528VG5taRMHwG0CDoAVSp4WclusZypxic/OhoNWacsoSn5S5SDbtpRxANwg4ACYYFw7Dts3+mmh2AVltov1jBRe4hJpyyi08WouH0BBBBwAcxQ+LZgh72YgTE5bRqGTV8u9M++V+Lk/9EP73wI0T8ABcJdx1fjIX/7L/UGJcl+p52DDgXC3Gw4aoy2j2LCTa5F7Zx4rsboDzRNwAFQu95V6DgyEyWnL8Po21snrZN2ZR0q838QB0DwBB8BJ41KyxO0bWa/Uc3BkWiAqbRmeNg4h6868q8TeqALQE3AAVCjrlXoODIQbcdED08khZP3AVGKAOQQcAMeNy8qCtm9kvVLPgWlhIzozMJ0cQtZtObPENnEAdAQcAJXIeqWeAwPhRnRmSH0b6+TV8m3LFSWWcQAIOACOGBeI+W/fyHelnoml00JqZ2fDQS10ZkiltHH28m1LJQZYTcABUDbL4aP6acHAsIV8Z8gSaeNA8m3LcCW2iQNonIAD4JBxaZjz9o18F+ubCzctMFfEtuzL2lRldXIgEdtypagl1jxAewQcAOXJd7G+uRIHwt1uOChcxLa8Udbqx7b+fKs/zVQyvY7RSrzfxAHQHgEHwC3jojPD7RvdKzP0HGYg3E7EtjxW1lprrY2DitiZi/Uljlxlb1QBmiXgAChDjiv1HCSZFjgmYlveWdbK6l7Z6WwtYmcutlWJ9RXQEgEHwHXjWjCf7Rs5rtRzsNW0wD2x2rIv6/TKVtADs86Xu8TqzDW2KLE3qgBtEnAA5CvHlXoODIRbi3L1F5e10Gboz7fQF5+l7lJmdzU3LbE3qgANEnAAXDGuAjffvpHjSj0Hm04LdKJ05vqyltUYZb3aEkRpyzX6EqsyQHICDoDRuBjdNt3IbqWegxamhbOz4SBXUTozbFnz75Dq2zi5KG25RmYltokDaI2AAyAX2a3Uc2AgzECUzoxU2Wy7RSeHFqUt18i/xDoQaICAA+CeceW3yfaN7FbqOch/WmhA+M7syxq1srl1Tm6vp3zh23KlvEvsp40CTRFwAGzM6HNTUwPhbjccZCb8DJm4rJu3UH++m7+MuoRvyzXKKbE3qgDtEHAA7Nd8ibdv5LVYz0Eh00LdwrflVmXdqpe0cQTh23KNokusOYGqCTgANpDXYn1z/bRg2b218G25eVkTv4DNz7dSGV3TYkvsjSpAIwQcQPPG1Wqa7RvdFzMA7RkI8xC4Lfuy5lPZBK8kq/OtSODOXKP8EnujCtACAQdAIhmt1HNgIMxD4LbMtqyRXlV/vnmecuECd+ZiSgxQFAEH0LZx2Rp1+0YuK/VMmBbyELgt8y9r2FeY//kWK3BnLlZjiW3iAKon4ACIKJeVeg76acGq+qCzs+EglZBlKKus61+qNo6mu6xZXNmqSyzjAOom4AAaNi7vYmzfyGWlnoOqp4XiBOvMvqwlVnbxay70fEsQrC1XUmKAwgk4AALLZaWeA9NCToJ1ZgVlnfX6+/Mt/ZRzFawtV2qpxDZxABUTcACtGhd2Abdv5LJSz0FL08Jyu91wEFmwzqyprFPOpabzzU+wtlyjL3HLVdbhQF0EHABhWCQ+y7SQma4SYYpRa1mPnZQ2jilYW67Rdon3mzgA6iLgAJo0rmuDbN/IYrG+OQNhZsK0ZV/Wuit74+yqP99NhWnLlZT4Hm9UAaok4ABYLovF+uZMC5kJ05ZNlbU/2aZOeQvbX1wlBqidgANoz7jAXbN9o/sUlsmmhdyEaUtlJbQwnblY39K6+habOID6CDgA5tl4pZ4D00J+wrSlshJamM5cTEvfRcYBVEbAATRmXMMt2L6x8Uo9B6aFGM7OhoNFwrSlyhJamM5cTEsDNEnAAbRk6Xp345V6DkwL+QnQln1ZVZagAnTmGlp6Jps4gJoIOIAWTd++sfFKPQemhSytLYmyEsGWD8y+pXX1Si4gULj7hn8CVG9ct01MN6zyrHTj2u2Gg5lvUbmsyv333feGL//yP/WH//DXfMmXPPJ5n/fZi4v/9/d+7//6zd88/9CH/vlv/Mbwh25TViLYsqu0dAi/9+f//HB0n+kAKJhHGNCMyQFH64tl00Ia8wOOq4X5L573vP/9G7/xjz3/+cPvr3vfRz7yXe9//5P/6T8Nv++pLBFs2VVaOigZB1ABb1EB2jAt3ej+UNPr5e4qGRiydKMz/+BDD/0f3/Itfbrx0ccf/0v/7J+98R/8g2//qZ969wc/+NS9UOM1L3rR33vd6+792bGsKktoN9oyKS0NwCECDoBB04tl00KuDs6Q/9PXfu2jz31ud/BTv/ZrX/1jP/ZX/sW/+OmPfOQnf/VX3/KBD7z0/Pw//O7vdv/qT/6hP/Rtf+JPKCsxHGzLFPonla6Ow08bBSog4AAaMK7Vjm3f2GyxngPTQq6OteUjDz74333lV3YHv/nJT37n+973zPXy/cYnP/mt//Af9sd/5iUv6Q8glGNtGZ0nVRIyDqB0Ag6gaZst1jfXTwuWsFk63ZZf+6Vf+jn33iH/U7/2a5/+/d/vP7h3cfF/f+xjH3vyye7wJV/8xf3HIIhtnheeVABMJuAAajeujG9s3zg9Q9bMtJCV6z9hdEpb/vanP/2PPvrR/+fjH/+Xv/mbw4c6fVnHyv7GE090//s59933wP2+0RPAlM4Mz8NqCzZxAEWz7gGas81KPQemhYxNb8tf+I//8Zvf+96v+dt/+yd/9Vef/f2tsj5w//393o3P/P7vP/PZz/YfhGWmd2ZIHlaZUAWgNAIOoGrj4qzfvrHNSj0HpoWMLW/LI2X9the/+HPvbdz4P//tv+0/Agss78zF+pb2sNrafhMHQGkEHEATNlip58C0kK3drv/nwtocL+vzH3rora94RX98/qEP9QcwywYPTE+qzHijClAoAQdQr3FZ9vlH/vKUmpkWsteVZ3aF+rIer+yDn/M5/+uf/tP/+UMPdcf/6KMf/cCv/3r/cZhoSVuu5GEFQDgCDoC6mBayt2SGnFDWB+6//3/7xm98+Qtf2B3/h9/93f/+H//j/uMwxZK2XMnDKm82cQAlEnAAlRoXZA1t3zAtZK8rz+wKTSvrww8++A+/6Zv+qy/7su74Y08++V//3b/7+Kc+1f8rOG1JW67Rt7SHVQlkHEBxBBwAhTMtlGDJDDm5rH/wuc/9mTe+8Wu/9Eu74//wu7/7yr/zd/q/JhZOW9KWa3hSARCZgAOo0biGrnz7hmmhBEtmyDmV/S+/+Iv/+Xd8x4sffbQ7/le/9Vtf++M/Lt3gTkvacg0Pq2LZxAGURcABUCDTQgnuniHPzoaDXl/WOZV99Yte9LPf8i2PPve53fHP/pt/86q/9/f+v6ee6v8VHHR3W4blYVUTpQSyJ+AAqjOuwOrcvmFaKEFXoXlFWlTWb3vxi9/zutf9Zw880B2/65d+6b/9iZ948umn+38FB6V7dvQt7WFVhf0mDoDsCTgACmFaKEFXoXlFWlrWN37lV77rT/2p/vh//Nmf/fMf+EB/THbyuG1nd+ZinlQ18kYVoBQCDqAu49qrnu0b/bRgTZm9rkJTi7TbDQdLy/o1X/Il//N/89/0x29473v/l3/1r/pj8nJ55256C8/ozJU2PU0A6Ag4gIqMa+tK0g3TQiHSDZD3PPg5n3P26lf3x9/zT/7J+z/ykf6YXPR37u2bN/ntnK4zD54vNbm4eO4P/uDl8XAAkJ/7hn8CVGBcdRUfcFg+lmNJqS53cDz22HAwx//wspf95T/5J7uD37+4+Mcf/Wj/wWO+46d/+tPPPDP8htim3Ln3pVh6JXqCeFK14HqVf+97v3c4StLJAHN5NgG1qCPdMDCUY2GpuhJ/93cPx4sCjn/5nd/5x57//OE3d3nBO9/pJ4+mMPfOjTYcJnqCeFJV70iJBRxA5rxFBSAD3VKy/0UJujrNLlW4Er/oi75oOCIHy8oaohNuWNKWCwRqY/J1ssTeqAJkTvgKVGFcaZW3fcMasShLqnW7xOt2cJCL9TdvoP8PPNFDxMOqetNKvN/E0bGPA8iMHRwAG+mWkgaGcnSlml2t0yWWbhSqL2uQm3f151nSlguEOl+yNafE+00cAPkRcADlG5dlxWzfMC0UpSvV7GopcZUilXXR51zSlnP15xvjlMnE0hJ7owqQLQEHQCpLl5JspSvV7GpNKbE2KE7sks385NG7R4tWT4mBSgk4gMKNS7Sst29YSpamq9a8gvUlnlLly78jliIku3mnfaHZnTlXsvNlK4FKbBMHkCcBB0BMpoXSdNWaVzAlrlJf1vSVPf4VZ3fmXJucLymFLrGMA8iQgAMo2bioynH7RuilJLF11ZpXMCWu0uZlvfXVZ3fmLP35bnvKRBWnxHHbEmApAQdAUHGWkkQ1e6WuxFXKp6zjK5ndmbPkc75EEqfEV9vyIZs4gMwIOIBijcupXLZvxFlKEtuMmvUlVuX65FfW7tVcxHtJ2rh6cUr8bFsOh4doKiADAg6A1UwLZbpjsX5VqBJf/Qmj3/Vdz/5iQ31ZM7t5r7Vl8NeW3/kSWJwSX2vL6/abOAAycN/wT4CyjAu4jbdvGBXKNKNsoUp851+ecnY2HJBAlnfuqdd037oFmydVC6JVecrnfep7v3c4WtmrAOt4BgFlGldymwUcBoYyzShbqBLfiDbe977h4DWvGQ5ukHREleWdO+k1LZsbPamqF7PE0z/1PuDoyDiA7XgAAQUa13MbpBumhWJNrVzYEh9LN66SdKSR5c077zXNmhs9rKoXs8QLPrVNHEAOPICAAo2ruqQBh2mhWFMrF7bEU6KNGyQdMeR65y5/WXdOjx5W1YtZ4jWfWsYBbM7TByjNuLBLl26YFoo1tXLBS7wg3bgk5ggl4zt37Ss7OD16UrUgZpXXf2oBB7A5Tx+gNOPyLkXAYWAo1tTKBS/xmmjjBknHYhnfucFe2dUB0pOqepFLHPCzyziAbXn0AEUZF3lx0w3TQskmFS9SiQOmG1dJOqbL+Ob1WGGJcqKNnp82CmzLcwcoR4J0Q7RRsknFKyvauKp75d/wDcPxDZKOTsY3r8cKS0Ru6Xif3SYOYEOeO0A5xtVelIAj4+mIKe6uX6QSx442Dr5sScelvO9cjxWWiNzVCdpSxgFsxUMHKMS44AufbuQ9IHGnu+sXr8RR0407X3bjMUfed67HCrPFb+lkbemNKsBWPHGAQowrv2ABR97TEVPcXcJ4Vd422rihtaQj75vXk4XZ4rd0+ra0iQPYhCcOUIJx8Rcm3ch7OmKKO0oYu8Tx0o2Vr7z6pCPvm9eThdmStPRWnSnjANLzuAFKMC4B1wYceU9HTHFHCWOXOFK0EfxlV5Z0ZH/nerIwW5Ku3rYzBRxAeh43QPbGVeCqdCP7AYk73VHC2CUuJdq4ofSkI/s715OFeVK1dCadKeMAEvOsAbI3LgeXBBzZT0dMcUcVE1Q5RrqRsjlLjDmyv3k9XJgnVUvn1pkyDiAlDxogb+OKcHa6kf10xBSnqpimxFF/mGgvZa8WkXSUcPN6vjBDqpbOsy0FHEBKHjRA3sZ14YyAo4TpiDudqmKyEidINxYIcvoZJh2F3LmeL8yQqqszb0sZB5CMpwyQsXFpODXdKGRA4rRTVUxW4jyjjWVOX7Qcko5C7lzPl8p1fRhw/E7V1UW05T7g6Mg4gJg8YoCMjQvEuwOOQgYkTjtVxZQlrindmO41rxkOboiadBRy53q+VO6yD9fP3glbuqy2tIkDSMMjBsjVuEw8lW4UMh0xxeFaJi5xm9HGVclijkJuXo+Ymt1uwjWzd8KWLrQtZRxAAp4vQK7GxeLhgKOQ6YgpDtcycYlFGzdESjrKuXM9Yqp1ogmXDd4Ju7rothRwAAl4vgBZGteLB9KNcgYk7nS4lulLLN04IVTSUc6d6xFTpykdOHfwTtvVFXSmjAOIzcMFyNK4arwWcJQzIHGnw7VMX2LRxnSLk45y7lyPmArNar+JU3fylq6pM2UcQFSeLEB+xrXjkG6UMx0xxYFyblVi6cZcfaWm/8Ur5dy8njK1WdZ7d47cyVu6vs4UcABRebIA+RlXkJ///d/fH1CHAyv1rQZg0cZctyt1OubYqrLzFfNCmWJl450YuZO3dMWdKeMA4vFYATIzLiKlGzU5sFLfagAWbcx1Z6WOJR2PPTYc5KriAbI5oZ4nB+dt0UZo+4CjI+MAgvJMATIj4KjLgZX6VtFGR7ox3YIyFZV0VD9DNiH4w+TqsL3Fk6qdtrSJA4jEMwXIiXSjIgdW6qKNIqwvU95JRzszZM0iPUz6YVu0kYSMA4jBAwXIhnSjFjdX6hvmGj3pxkTBK3U16bj6yef+FbOBbN2IrLb5wySCZttSwAHE4IECZEPAUb6bK3XRRimiVmrx3y8bTrMz5EJdP2Q1c9aYa3S0pYwDCM7TBMiDdKN81xbrOQwk0o07JS7TFkmHGXKeqy2x+cxZaa7R0ZaXZBxAWB4lQB4EHCW7tlgXbRRh2zIlSTrMkPMca4n0Y2e9uUZHW94g4ADC8igBMiDdKNZ+sZ7JTCLauFNW02OcpMMMOc+dLZFm8qw61+jpzINkHEBAniNABgQcBdqv1PMZS6Qbp+U8QAZKOgyQ80xviXiTZwO5RkdnnrAPODoyDmAdDxFga9KN0uxX6qKNIhQ0QK6IOQyQMyxuiYDDZxu5RkdnTmETBxCKhwiwNQFHOfYr9ayGE+nGMeXOkHOSDgPkDOtbYv38KdrgEBkHEIQnCLAp6UYhhjrlNpmINo6pZoa8K+kwQ04VsCWWzZ/N5BodbbmAgAMIwhME2JSAI3tDhUQbpah1jLyVdAznue7HkTYhUktMnEJbyjU6bZ1taDIOYD2PD2A70o28DeXJcD6RbtzWzhj5mtccPlVJxw0JWuLEFNpYrtFp7oTjkHEAK3l2ANsRcORqKIxoowgtTZL7Uw30t67UKWVL3JhC28s1Oi2eczQCDmAlzw5gI9KNXF1kO6JIN25oM9q4QdJx1VYtcTmLNhZwtHW2qcg4gDU8OICNCDjyI9oohmjjtsaTjs1bop9Fm+nMhu7A5PYBR0fGAczkqQFsQbqRmXyjjY504yrRxp2aSjqy6oduFm2gPxu6A7dycfHUW986HAs4gJk8NYAtCDiyIdooQ0u5RifM2daddDTWEplw0eO60tUyDmAZjwwgOelGHkQbZRBtrFRfzCHa2IKLHtGhlhZwAMt4ZADJCTi2lXWwcY90oyfaCKuCpEO0sQUXPaKTLS3jABbwvADSkm5sSLRRCtFGVMUlHXKNjbjuEU3rahkHMJeHBZDQlQWNgCOp/KONjnSjyTl2y3POP+kQbWzEdY9oTlcLOIC5PCyAhMZljXQjHdFGEUQb28ow6RBtbMR1j2VpS8s4gFk8KYBUpBsp3bvaBazURRuijXxkEnOINjbiuseyrqX3AUdHxgHcxWMCSEXAkUYp0Uan8XRDtJGtrZIO0cZGXPdYArW0TRzAdB4TQBLSjQTGi1zAYr3laKPVIbbI006TdMg1tuPSxxK6q2UcwESeEUASAo6oCoo2Os2mG6KNckVKOkQb23Hpo4jW0gIOYCLPCCA+6UYkV5aSZSzWRRuNqfC0QyUdoo1NufrhxW9pGQcwhQcEEJ+AI7jioo1Om+mGaKNKa2IO0camXP3wEra0jAO4k6cDEJl0IyzRRhEaHmIbOvOuyt/wDcPxDbeTjoZbIhMKEF7yrhZwAHfydAAiGxdAAo61riwli1mpizZa0sqZHyzxiaSj4ZbIhAIEtmlLyziA0zwagJjGZZB0Y7nrS8mSVuqtpRsNz7GtnPmUEh9LOh57bDggoXbvyUgyeMrtA46OjAO4xXMBiEnAsYZooxQNRxudJk5+QYklHZtq+p6MIaennE0cwAmeC0A00o3Fyo02Ok2lG6KN6q0ssZgjuabvyRiyfMrJOIBjPBSAaAQcC4g2itB2rtGp//yDl/hG0nH5+W/8ONLLaa35HlvAJQss4yYUcADHeCgAcYwLI+nGVNeXkoWt1EUbzaj//GOX+PRfMdtNa8332AIuWUiFdKCMAzjIEwGIY1whCTjucGgpWdhivZF0o/mxs/7zT1zi00kH07R+W4ZV2lNOxgHc5nEARCDdmEK0UQrRxvDPem1bYknHIq3flmGV+ZQTcAC3eRwAEQg4Tqsg2uhUn240n2t0Kr8EWZVYzDGHmzOYwh90Mg7gBs8CIDTpxgmijSKINkpsy1lyLrGk4yQ3Zxi1POX2AUdHxgEIOIDwBBy3HVlKFrnAvJpuiDZqVPklKKjEko7r3JxhVPeUs4kDuMqDAAhKunFDrdFGp7J0Q7RRaFtOV26Jm0863Jxh1PuUk3EAlzwFgHCkG1eJNoog1xjVfCGqqXJ7SYf7M4zaH3TeqAJc8ggAwhFw9GqKNjrV/8SNS62GHdWedsUFPZh01BVzNHo3htXSM80mDqDnEQAEIt04vpQsdY3ZTrSxTPnDQ7XTTyNzXaUbOtooXmQtRRuXZBxAx/0PBNJywFFftNGRbgSX08hR7fTT5FxXTdLRZPFCa/MWuEfAAXTc/0AIzaYbog3iiTOoVDv9NDzX7RWbdCheAG4BGQcg4ADCaDDgOLmULHWZKdooXZVteZqh7qBykg71W8stcJ2MAxrnzgdWayrduGspWfBKU7pRNNEGB2X840jVby23wCECDmicOx9YrZGAQ7RBnkQb3Cm/DR2BS3jZEo3MtG6Bk2Qc0DK3PbDOuMyqOd24aylZ9kpTulGuk51Z5wBkrlspg6QjcAlvt0TdM61bYIJ9wNGRcUBj3PPAOuNiq86A466lZNkrTdFGuU52ZoUDkKEuuC2SjpBVvLMl6htr3QVz2MQBzXLPAyuM660K0427lpJlrzRFG4Wquy2XMfWtlCTpCFmk6RWvY7LV4UvJOKBNbnhghXHhVU/AMWEpWfxiU7pRohY6Mw3j4jFxfhxpyMu9oHZFT7Z6dR0BB7TJDQ8sNa69Kkk3WhggRRslaqEzc9bakBluQ0fIC7eyCsXNt611XTQyDmiQux1YalyBFR9wNDJASjeK00hn1qeO6XRF0hHs/ANeyVLm2zqaJycyDmiNWx1YZFyElZ1uNDJAijbKMm3CMQYVrKwhdk7SEezEYlyinOfbslqiKAIOaI1bHVhkXI0VGXBMXkrWsOSUbhRkWmeahApW9Bx7MukIdmKxL1FuU27RLVGC7vp+SsYBLXGfA/ONC7Ly0o3JS8kalpyijYJM68wa2rJZNc2x15OO4cRW/zjSdJcokym3ppbI0uX13QccHRkH1M5NDsw3LstKCjgmLyVrWHKKNgoyrTNraMtm1TrH3os5Dpzb3KRjk+uz7ZRba0tk4/b1tYkD2uEmB2YaV2bFpBuTl5KVLDmlG0VorS3bVPUcuz+3xT+OdPPrk3jWrbofMnHiEss4oBHucGCmcYmWe8AxZylZyapTtFGEyZ1ZSVs2qPY59ujpTU868rlEaWbd2lsiB3deYgEHNMIdDswxrtKyTjfmLCXrWXVKN/I3uTPracvW1D7HTj29E0lHhpco6rhbe0vkYPollnFAC9zewGTjQi3fdGPOUrKeVadoI3+TO7OetmxN7XPswtM7mHQ89thwkJXgE69oI74Fl1jGAdVzbwOT5RxwiDY6oo3czJxw6unMpog27nRsQ0duSUeQiVeukcTiqyzggOq5t4Fp8kw3Wh4gpRs5E21Ur4E5NvwZ5p90rBl6RRtJrL/KMg6omxsbmCa3gEO0cUm0kRXRRvVEG+vdSDouL+ncv2I2krlzbwMtkYkgF3ofcHRkHFAddzUwwbh6yyLdaHyAlG5kq/HObEEDc2zqM3z1q4eDGzZPOibOvaKNVMJeaJs4oGLuamCCTAKO+UvJqtaeoo1siTaqJ9qI7WDSsW3McXr0FW2kEulCyzigVm5p4C45pBuNRxsd6UaGtGX12hhiMzrJDDd03Jh+5RoJRb3WAg6olVsauMuGAceipWRty0/RRoZEG9VrZo7N9DyzSjr6AVi0kVCaay3jgCq5n4GTtko3RBsd0UaGRBvVE21kJdsf0kEcidtSxgH1cTMDJ6UPOEQbPelGbkQb1RNt5EzSUbtN2lLAAfVxMwPHJU43RBs90UZWtGX1msk1OjWcaoY/jpR1NmjLK3f9p/7CXxiOZBxQBXcycFyagGPpdFHDSv026UY+dGb1RBvlsqGjChu05a27fh9wdGQcUD63MXBEgnTDAHmVaCMfOrN6oo1qSDrKtEFbHr/rbeKAmriNgSOiBhwGyKtEG/nQmdUTbdRK0lGIDdpywl0v44BquIeBQ+KlGwbIG6QbOVgx9FbbmfURbVSvL/FrXnPvN7dIOjKQujMn3/UCDqiGexg4ZFwTBAs4DJC3iTZyoDOrt6LEJWqxLY+V+GDSIebYSNLOXHTXyzigDm5g4JZxZRAm3Vg3XSRdEqUk3djcis6sti0rs+7hU5wW23JKiW3o2FrSzlx318s4oALuXuCWcX2wNuBYt85IuiRKSbSxuRWdWW1bVmbdw6c4LbblghJLOpJL2pkh7noBB1TA3QtcNy4RVqUb69YZSZdEiUk3NqQtWxBiyClLeye8+owlHfElbcugd72MA0rn1gWuuLJKWBJwrF5kJF0SJSba2NC6zqy5LasRdMIpRVvnHKPEko4I0rVlnLt+H3B0ZBxQIPctcMW4XJidbqxeZ6RbEqUn2tjQus6suS2rEWfIyVxb55ygxH4caQjp2jJyS9jEAUVz3wKjccUwL91Yvc5ItyTahHRjK+s6s/K2rEOCuTc/bZ1z4hLb0LFUujqlagkZB5TLTQuMxnXD1IBj9Toj7dI1OdHGVnRm9RLPvXlo65y3LbGkY7J0dUrbEgIOKJebFrhnXDpMSjcMkHeSbqQXYvlbf2cWbduhdzttnXZWVZZ0HJeoTtv1g4wDCuWOBe4Z1xCnAg4D5BSijfR0ZvWyGnoTaui0My+xpOO6FNXKoCVkHFAityuwX0YcTTcMkFOINtLTmdXLfO6NpqHTLqvEzf840hTVyqYlBBxQIrcrsF9MHAg4Aq0zilrALiLdSCxEZ9bflkUra+4Np6HTLrfETW7oSFGt/FpCxgHFca9C88b1xM10I9A6o9gF7GSijZS0ZfXKHXpXa+jMq6lyG0lH9Gpl3A/7gKMj44ASuFGheePCYgg4wq0zalnAnnQj3Xj/+4eDYxoe3tYKdOkUIF8N3x2tnHnFJa406YhesBJawiYOKIsbFdo2ri2eTTfCrTPqXcNeMTfaWKbhkW8v0EVwKfPVdp83cfLtlLiWpCN6wYpqCRkHFMRdCm0bVxif/5f+Un+wUitr2DTpxg0NDoGBTrm9C1eOBrv6iiZOvtkSF/vjSKMXrMCWEHBAQdyl0LBxkREk3WhlDSvaSCDc+TZ24YrS7Nx7TxMn33aJByc2dFxen2xm5ugFK7klZBxQCrcoNGxcaqwMOFpZw6aPNhocD8KdcnvXrhANdvV19Z9/8yU+7FjS8dhjz/7v1jNz3JrV0hIyDiiC+xNaNS441qQbDS1jE6cbDU4IQU+5vctXgubn3vrPv/kST5LZD+mIW7O6WkLAAUVwf0KrxmXHsoCjoWWsaCOxdVeg+cuXpea7uv7z9+BaYOukI27NKm0JGQfkz80JTRpXHgvSjbaWsSnTDRPCYvcuncuXo+a7uv7z9+Ba72rScXk9z8+Hgzgilq3qltgHHB0ZB2TJnQlNGtcfswKOtpaxyaIN48Fqs6+gax6bK1z9A1OJg3v1q4eDG0InHbEq10xL2MQBmXNnQnvGVYh04zDRRjkSXUGVms61qv5pqcSxRUs6YlWuvZaQcUDO3JbQnnEtMjHgaGvlkibdMCGslvUVbLO+urr6p6USJxYu6YhVuVZbwhtVIGfuSWjMuByZkm60tXIRbRQi9yvYYIl19T01XwUl3taKpCNW5ZpvCZs4IFvuSWjJuCK5M91obuUSO90wHoSQ+0Vsrcq6elTzhVDlrBxMOo7EHFEqpx+ukHFAntyQ0JJxaXIi4Ghu8SLaKEHWF7HBEuvqUbUXQolzdteGjijF0xK3CDggT25IaMa4OjmWbrS4eImablgOhpD1RWywxLp6VO2FUOKC3Eo6huKt/nGk12iJ42QckCF3IzRjXKPcDjhaXLyINkqQ73VU4tuauSbVnqeuLterX324eCuTDi0xgYwDcuNWhDaMy5Qb6UaLixfRRgnyvY5KHEqBV7La2uvqkl0rXpC/eEU/zCHggNy4FaEN43rlMuBodP0SKd2wHAwn00upxJvbtAR1ll9XF+5U/eb8ONI9LbGIjAOy4j6EBoxLlj7daHT9ItrIXqaXUokLFahwdZZfV5fvjhL2JX7Na+795pbbSYeWWGEfcHRkHLA1NyE0YFy4PHzkx4vWL0a6YTkYTqaXUomrd7LEdZZfV5fvjhIeLPGJpENLhGATB+TDTQi1G9cujaYboo28ZXoplbh6J0tcZ/l1dfnuKOGUEh9LOs7OhgOWknFAJtyBULtxxdNcwBE82jAeBJXj1VTiFpyscoUdoKurcEcVF1RZ0hGagAMy4Q6Eqo2LHunGcLCMCSGoHK+mEldvQolrawJdXYVTVQxS4oNJh5hjERkH5MDtB1UbVz8NBRyijYzleDWVuHoTSlxbE+jqKpyqYvAS29ARiIwDNufeg3qNCyDpxhImhKByvJpKXL0JJW69CdwFWTpVldglk3SsI+CAzbn3oF7jMqiJgCNUtGG5H1p2F1SJWzChyvpgCbdPZKeub+KLL+lYSsYB23LjQaXGlZB0YyoL9wjyuqZKXL1pJdYH6bjpJjt6pTa/hpKOmfYBR0fGAcm566BS45Ko8oBDtJGrvK6pEldvWon1Qe6avFWPnnNuV8OPI53MJg7YkLsOajSuimpON0Qbucrrmipx9aaVWB8UrOq7+PC55XzKNnRMI+OArbjloEbj2qjagGNlumHojSOvy6rK1ZtWYn1QsKrv4sPnVtApSzpOEnDAVtxyUJ1xeVRnuiHayFJGl1WJqze5xFqhYFXfyAfOrejzlXQcdHHxqe/7vuFYxgEJud+gOuM6qcKAY026Ye6NI6PLqsTVm1xirVCq2u/iA6dX0ylLOjrXCyrjgPTcbFCX8TtrbemGaCM/GV1WJa7e5BJrhVLVfhefOr36zr3ZH0d6q5QCDkjPzQYVGb+zVpVuiDbyk9FlVeLqzSmxbihS7Xdx+NMr5Yo1uKHjUGlkHJCYOw0qMn5nrSfgWJZu1L5c3lAuV1aJqzezxBqiSLXfyB6Yg3aSjkOXeh9wdGQcEJ/bDGoxflutJN0QbWTGSp1EZpZYQ5Sngbu47DOMV6Dqk44jl84mDkjJbQa1GL+t1hBwLEg3GlgxbyWXK6vE1ZtZYg1Rngbu4hbbckFZa006jl8KGQck4x6DKozfU4tPN0Qbmcni4ipx9WaWWEOUp4G7uPW2XFbiyn4c6fGLIOCAZNxjUIXxe2rZAcesdKOB5fK2tr++StyCmVXWE+Vp4EZuvS3Xl7iaDR0nL4WMA9Jwg0H5xm+oBacboo2cbH99lbh680usJwrTzF3cdGcGr/KNpOPy85+fDweZu+uCyDggAXcXlG/8hlpkwCHayMn211eJqze/xHqiMM3cxe12ZoISv/rVw8ENmScdd10ZAQck4O6Cwo3fTStPN5pZMW9l++urxNWbX2I9UZhm7uJ2OzN9ictKOiZcHxkHxObWgsKN300LCzgmRhvNLJc3tP0lVuXqzS+xnihMM3dxu525eYkPJh35xByTr88+4OjIOCAC9xWUbPyGWmG60cxyeUMbX2Ilrt7SEuuMYrR0F7fblllVOcMNHfOvj00cEJX7Cko2flstJuAQbeRh40usxNVbWmKdUYyW7uJG2zLzEueQdKy4RDIOiMdNBcUav7OWkW6INvKw8SVW4uotLbHOKEZLd3GjbVlWiTdJOlZfIgEHxOOmgmKN318LCDhOpxstLZc3tPFVVuXqLS2xzihGS3dxo21ZdInTJB3hLpGMAyJxR0GZxm+xuacboo0MbHmVlbh6K0qsOYrR0o3caFvWVOIYP440zvWRcUAMbico0/i9NuuA40S60dJyeVubXWglrt6KEmuOMjR2F7fYlhWXONSGjpiXSMABMbidoEDjt9t80w3RRgY2u9BKXL0VJdYcZWjsLm6xLdsp8eKkI8klknFAcO4lKND4TTfTgONYutHYinlDm11oJa7eihJrjjK0dxe3d8Kt3ovTk46El2gfcHRkHBCCGwlKM37fzTHdEG1sbZsLrb7VW1di/VGG9m7k9k7YvXjPsaTj7Gw4SMsmDgjLjQSlGRcoeQUcp3+Y6FwWYfNtc8lUqnrrSqw/CtDkXdzWOXtQH5NN0iHjgIDcRVCUcZlSc7qxTMMLuG3O3Iq5eutKrD8K0ORd3NY5e1BPkUHMIeCAgNxFUI5xpZJRupFDtLFMFcu+bc7Birl6q0usRXLX5F3c1jl7UC+wRdJxWadPyzggELcQlGNcr+QScJSbbiyQ2WJxg1djudyC1VXWJblr8kZu65w9q9dLknTcrpOMA4Jw/0AhxiVLFulGU9HGDVuvHTf48pbL1QtRYl2StVbv4rZO27M6uGhJx8FSCTggCPcPFGJcuGwccIg2trPBl7dcrl6IEuuSrLV6Fzd02h7UCYRLOk5XS8YB67l5oATj8kW6sY0Mlo+pX4EVc/VClFiXZK3Vu7ih0/agTmxdzDGlWvuAoyPjgEXcOVCCcRGzWcAh2thO6ldgxVy9ECXWJVlr9S5u6LQ9qLc1M+mYVS2bOGAldw5kb1zHSDfSyWPtuPGLsICuTKCCaot8tX3PtnLynsxZuSvpWFYtGQes4baB7I2rmQ0CDtHGRopcwFp2ZytQaRQ4X23ffU2cvAds5m4lHUPBFv04UgEHrOG2gbyNaxrpRnR5LB/bWsNasscW6AqrU77avomaOHnPybK8+tWHCzYz6ZBxwGLuGcjbuLJJGnCINrZgDXs3C/3pAl0rVzxfbd8OTZy8J15p9gUL8beuyDhgGTcMZGxc3KRLN5qKNrJZO1rDxtLgeBDulLVlvtqee5s4+bZLXKKjBVuRdAg4YBk3DGRsXOIkCjjaSTeyWTtaw8bS4HgQ9JR1Zo6aH3rrP//mS1yiqTVblHTIOGABdwvkalzopEg3RBvJWcbG0uCEEPSUdWaOmp976z//5ktconk1uyzxa14zHNxwKOnYBxwdGQdM41aBXI3fC6MHHI2kG9ksHy1jY2lwQgh6yjozRw129XX1n3/zJS7UjLIdK/G0pMMmDpjLrQJZGr8dxk03RBtpWcbG0uCEEPSUdWaOGuzq6+o//+ZLXKgZZZtS4gkxh4wDZnGfQJbGb4qxAo4Woo3M1o5WsuEZD26beU1cwezo6urbUomLNaNyC6p8POnwRhWYxU0C+Rm/L0o3Fsps+WgxG54JYbXhCrqS+VCL6p+WSlysqZULUuJDScenH310OBJwwF3cJJCf8Rtk+IBDtJGWxWx4JoTV1l5BJQjOJb2n5qugxMWaWrkIJf70d37ncHSDjANOcodAZsbvkdKNeTJbPlrMhmdCWG2bK6hwJ7g499R8FZS4WBMr9+k3vWk4SkbAASe5QyAnV1ZCIQOOiqON/NaOFrOBGQ9CyP0itlZlXT2q+UKocjY+lT6DiErAASe5QyAn43pIunG3/NaOFrOBGQ9CyPoiNlhiXT2q9kIo8VK1xRBTZB9V/PE//sc//OEPP/XUU4888sjwIciegAOyMa6KgqUboo1UrGcDMyEEku91bLDEunpU7YVooMQtZhCdVndMPPzww7/wC7/w4he/+JOf/KSAg4IIOCAb49ooQMAh2kjFyBKYITCQfK9jgyXW1aNqL0RmJbYVgvUeeuih973vfa985Su7YwEHZfE4gDyMyyPpxgFZjgdGlsAMgYHkex1bK7GWvqLaa7G0yrZCkLNHH330p3/6p7/6q7+6/62Ag7J40EAexkXSqoBDtJGEqSUkQ2A4mV5KJb5T1Zeo6HP71Hd8x3DUDhlE897whjf86I/+6POf//zh9wIOSuMpBhmQbtwm2qieuTecTC+lEsdTwrVN8xJbzCA6YggieMlLXvI3/sbf+Jqv+Zr+t3/zb/7N17/+9c9//vMFHJTF8xEysDLgEG0kYVYLxtwbTq53ixJnJm1Fbn8xWyEgf+9617ve/OY3dwe/9Vu/9ef+3J/7iZ/4iU984hMCDorj4QtbW5Nu1BRtZDwRmdWCMfeGk+mlVOJiPfVn/sxw1BQxBIze9a53ffu3f/uP/MiPvP3tb3/yySe7jwg4KJHHOmxtccBRTboh2qieoTeoHK+mEqfSYgwhg4Akvuqrvupf/+t//du//dvD7wUclMn3DNjUsnRDtBGfcS0Mc29QOV5NJb7FVgigDgIOSuS7EWxqQcBRR7oh2qieuTeoHK9m4SW2FQLgNAEHJfKtDrYzN90QbURmIg9DtBFUjlczVYlthQDYkICDEvkmCtuZFXCUnm7kPfSayAOQa0SQ3TU9VGVbIQCqJOCgRL5Dw0ampxuijZgM5QGINiIIe02f+vZvH47aIYMAWEfAQYl8+4eNTAk4RBsxGcoDEG0E9XtiCACyIeCgRBYWsIXq0w3RRvVajTZkEAA0QsBBiaxaYAunA45yo40Shl7pxiollLjFDKIjhgAgKAEHJbIeguSqTDdEG9ULXWJbIQAgZwIOSmSxBckdCzhEG9GINpb5vW/7tuGoKWIIABBwUCbLOEjrYLoh2oimhWijxRhCBgEAkQk4KJE1IiR0O93oPvLd3z0c9/JPN0rINTpZvUpbIQCAsgg4KJHVJyR0NeAQbUSz+FXaCgEA0BNwUCJLW0jlMt34i3/x2X+UlW5kE208aSsEAEB8Ag5KZNEMqVwGHI8/3h8Maow2WowhZBAAALApK3JI4mC6sWm08eS3futw1BQxBAAAVMpaH5K4HXBMSzdajCFkEAAAwHwGCYgvmx9gEZIYAgAAyMn9wz+B5zznTW9608/8zM888cQTTz/9dPe/3fF3fdd33X9/sbfJffdF/AUAAADk5gUveMEHP/jBi0N+5Vd+5Y/+0T86/LllLi5O/QIAAABY7+GHH/7IRz7Sxxm//Mu/vNvtXvva177pTW/6xV/8xf6DH//4xx999NHhTwMAAABk6G1ve1sfZLz3ve+98YaUH/3RH+3/1fn5+fAhAAAAgNw88MADTz755MXFRfe/jzzyyPDR0f333/+xj32s+7dPP/109yeHjwIAAJAZP2SU1n3d133dc5/73O7gJ3/yJ5944on+g5c++9nP/vzP/3x38Lmf+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Sequences 23: Hat Guessing Game!","description":"Consider the following Game Show:\r\nHats, with numbers written on each, were placed on the heads of the participants. Participants can see the numbers on all hats, except their own. Each participant were asked to add all the numbers they do see and write the sum on a piece of paper card. The participants were then asked to hide their hats and show only their cards with numbers, to you, the contestant. For a prize of a million dollars, you were asked to guess the numbers written on each participant's hat.\r\nAssuming that all sums are correct, will you be the next millionare? Let's find out...","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 144px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the following Game Show:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eHats, with numbers written on each, were placed on the heads of the participants. Participants can see the numbers on all hats, except their own. Each participant were asked to add all the numbers they do see and write the sum on a piece of paper card. The participants were then asked to hide their hats and show only their cards with numbers, to you, the contestant. For a prize of a million dollars, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eyou were asked to guess the numbers written on each participant's hat.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eAssuming that all sums are correct, will you be the next millionare? Let's find out...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function nums = hatNumbers(sums)\r\n    nums = sums;\r\nend","test_suite":"%%\r\nsums = [667 658 645 688 629 625 713 630 637 678];\r\nnums_correct = [63 72 85 42 101 105 17 100 93 52];\r\nassert(isequal(hatNumbers(sums),nums_correct))\r\n%%\r\nsums = [1460 1459 1394 1416 1411 1428 1439 1394 1393 1395 1471 1470 ...\r\n        1469 1468 1395 1408 1407 1408 1395 1384 1439 1428 1406 1395 1460];\r\nnums_correct = [23 24 89 67 72 55 44 89 90 88 12 13 14 15 88 75 76 75 88 99 44 55 77 88 23];\r\nassert(isequal(hatNumbers(sums),nums_correct))\r\n%%\r\nsums = [ ...\r\n4892 4927 4901 4949 4896 4963 4939 4962 4957 4884 4897 4935 4871 4963 4923 4928 4890 4887 4948 4918 ...\r\n4922 4902 4896 4891 4939 4899 4901 4950 4955 4917 4871 4932 4908 4944 4891 4941 4916 4897 4877 4871 ...\r\n4912 4953 4952 4941 4882 4941 4885 4942 4874 4932 4947 4941 4905 4919 4931 4883 4908 4912 4875 4938 ...\r\n4891 4891 4928 4910 4959 4961 4913 4889 4873 4954 4910 4920 4965 4933 4950 4887 4935 4914 4950 4906 ...\r\n4940 4901 4898 4892 4921 4958 4944 4875 4951 4884 4913 4867 4959 4922 4956 4870 4966 4889 4885 4880 ...\r\n];\r\nnums = hatNumbers(sums);\r\nnums_stats = round([std(nums) mean(nums) mode(nums) median(nums)],4);\r\nassert(isequal(nums_stats,[28.8090 49.6700 26.0000 50.5000]))\r\n%%\r\nnums = randi(1000,1,1000).*97+2;\r\nsums = arrayfun(@(n) sum(nums(n-1:-1:1))+sum(nums(n+1:end)), 1:length(nums));\r\nassert(isequal(hatNumbers(sums),nums))\r\n%%\r\nfiletext = fileread('hatNumbers.m');\r\nblocked = {'solve' 'fsolve' 'dsolve' 'linsolve' 'mldivide' 'mrdivide' '\\' '/'};\r\nnot_allowed = any(arrayfun(@(s) contains(filetext, blocked{s}), 1:8));\r\nassert(~not_allowed)\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2021-09-24T08:03:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-22T11:19:54.000Z","updated_at":"2025-12-07T16:32:52.000Z","published_at":"2021-09-24T08:03:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the following Game Show:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHats, with numbers written on each, were placed on the heads of the participants. Participants can see the numbers on all hats, except their own. Each participant were asked to add all the numbers they do see and write the sum on a piece of paper card. The participants were then asked to hide their hats and show only their cards with numbers, to you, the contestant. For a prize of a million dollars, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eyou were asked to guess the numbers written on each participant's hat.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssuming that all sums are correct, will you be the next millionare? Let's find out...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60981,"title":"Mesh the pentagon (with the minimum number of triangles)","description":"Problem statement\r\n\r\nAn pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set V, corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.\r\n\r\nV = [1           0            0;\r\n     cos(2*pi/5) sin(2*pi/5)  0;\r\n     cos(4*pi/5) sin(4*pi/5)  0;\r\n     cos(4*pi/5) sin(-4*pi/5) 0;\r\n     cos(2*pi/5) sin(-2*pi/5) 0];\r\n\r\nA triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, F. The row order of the triangles in the list doesn't matter.\r\n\r\nExample\r\nThe first triangle here can be [1, 2, 3] if counterclockwise oriented.\r\n\r\n\r\n\r\n\r\nTip\r\nBeware to avoid self intersecting triangles.\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1278.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 639.2px; transform-origin: 408px 639.2px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 327.525px 8px; transform-origin: 327.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.09167px 8px; transform-origin: 6.09167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2417px 8px; transform-origin: 48.2417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 51.0833px; transform-origin: 405px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eV = [1           0            0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(2*pi/5) sin(2*pi/5)  0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(4*pi/5) sin(4*pi/5)  0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(4*pi/5) sin(-4*pi/5) 0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 127.05px 8.5px; tab-size: 4; transform-origin: 127.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(2*pi/5) sin(-2*pi/5) 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.983px 8px; transform-origin: 176.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.633px 8px; transform-origin: 132.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384.442px 8px; transform-origin: 384.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.25833px 8px; transform-origin: 7.25833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eF. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.8583px 8px; transform-origin: 89.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 339.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 169.75px; text-align: left; transform-origin: 385px 169.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"445\" height=\"334\" style=\"vertical-align: baseline;width: 445px;height: 334px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.3667px 8px; transform-origin: 10.3667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTip\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 131.092px 8px; transform-origin: 131.092px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBeware to avoid self intersecting triangles.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_pentagon()\r\n  T = 1;\r\nend","test_suite":"%%\r\nT_correct1 = [1 2 3;\r\n              1 3 4;\r\n              1 4 5];\r\n\r\nT_correct2 = [2 3 4;\r\n              2 4 5;\r\n              2 5 1];\r\n\r\nT_correct3 = [3 4 5;\r\n              3 5 1;\r\n              3 1 2];\r\n\r\nT_correct4 = [3 4 5;\r\n              3 5 1;\r\n              3 1 2];\r\n\r\nT_correct5 = [5 1 2;\r\n              5 2 3;\r\n              5 3 4];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct1,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct2,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct3,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct4,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct5,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_pentagon.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":149128,"edited_by":149128,"edited_at":"2025-08-13T05:29:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":"2025-08-13T05:29:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T12:59:46.000Z","updated_at":"2026-02-10T17:07:57.000Z","published_at":"2025-07-23T15:54:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[V = [1           0            0;\\n     cos(2*pi/5) sin(2*pi/5)  0;\\n     cos(4*pi/5) sin(4*pi/5)  0;\\n     cos(4*pi/5) sin(-4*pi/5) 0;\\n     cos(2*pi/5) sin(-2*pi/5) 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"334\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"445\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTip\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBeware to avoid self intersecting triangles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/57483\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh 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Mathematics 4","description":"Team #1 is in first place but only one point higher than Team #2.  The sum of their two scores is N. What are each team’s scores?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTeam #1 is in first place but only one point higher than Team #2.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe sum of their two scores is N. What are each team’s scores?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [team1, team2] = teamPoints(N) % Do not edit this line.\r\n  % insert your code here\r\n  team1 = ?;\r\n  team2=?;\r\nend % Do not edit this line.\r\n","test_suite":"%%\r\n[team1, team2] = teamPoints(147);\r\nassert(isequal(team1,74),\"team1 points correct\");\r\nassert(isequal(team2,73), \"team2 points correct\");\r\n%%\r\n \r\n[team1, team2] = teamPoints(285);\r\nassert(isequal(team1,143), \"team1 points correct\");\r\nassert(isequal(team2,142), \"team2 points correct\");\r\n%%\r\n \r\n[team1, team2] = teamPoints(91);\r\nassert(isequal(team1,46), \"team1 points correct\");\r\nassert(isequal(team2,45), \"team2 points correct\");\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":542228,"edited_by":542228,"edited_at":"2022-09-13T17:29:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":363,"test_suite_updated_at":"2022-09-13T17:29:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T15:38:54.000Z","updated_at":"2026-03-30T16:36:17.000Z","published_at":"2022-09-13T15:38:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTeam #1 is in first place but only one point higher than Team #2.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe sum of their two scores is N. What are each team’s scores?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44530,"title":"Are you more familiar with iteration methods or Linear Algebra? Let's see together.","description":"Given a sum result *_x_* value of a *_N_* number of addends, build an array of _*N*_ elements _*y*_ such that the following equality is satisfied: _sum(y) = x_ .\r\n\r\nFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].\r\n\r\nMore formally if x = a and N = n it results: \r\n\r\ny = [y_1 y_2 y_3 ... y_n]\r\nwhere:  y_1 + y_2 + y_3 +...+ y_n = a\r\n\r\nImportant notice: All the elements in y must be *different from zero* and *different from each other* . On the other hand I will not take into account if they are _integers or decimal numbers_ .\r\n\r\nHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\r\n\r\nGood luck and enjoy with the solution ;)\r\n","description_html":"\u003cp\u003eGiven a sum result \u003cb\u003e\u003ci\u003ex\u003c/i\u003e\u003c/b\u003e value of a \u003cb\u003e\u003ci\u003eN\u003c/i\u003e\u003c/b\u003e number of addends, build an array of \u003ci\u003e\u003cb\u003eN\u003c/b\u003e\u003c/i\u003e elements \u003ci\u003e\u003cb\u003ey\u003c/b\u003e\u003c/i\u003e such that the following equality is satisfied: \u003ci\u003esum(y) = x\u003c/i\u003e .\u003c/p\u003e\u003cp\u003eFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].\u003c/p\u003e\u003cp\u003eMore formally if x = a and N = n it results:\u003c/p\u003e\u003cp\u003ey = [y_1 y_2 y_3 ... y_n]\r\nwhere:  y_1 + y_2 + y_3 +...+ y_n = a\u003c/p\u003e\u003cp\u003eImportant notice: All the elements in y must be \u003cb\u003edifferent from zero\u003c/b\u003e and \u003cb\u003edifferent from each other\u003c/b\u003e . On the other hand I will not take into account if they are \u003ci\u003eintegers or decimal numbers\u003c/i\u003e .\u003c/p\u003e\u003cp\u003eHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\u003c/p\u003e\u003cp\u003eGood luck and enjoy with the solution ;)\u003c/p\u003e","function_template":"function y = buildSumArray(x,N)\r\n  y = sum(1:N);\r\nend","test_suite":"%% Test Case 1\r\nx = 6;\r\nN = 3;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n\r\n%% Test Case 2\r\nx = 13;\r\nN = 5;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n\r\n\r\n%% Test Case 3\r\nx = 78;\r\nN = 11;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n\r\n\r\n%% Test Case 4\r\nx = 2689;\r\nN = 245;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":181340,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2018-02-24T12:07:13.000Z","rescore_all_solutions":false,"group_id":677,"created_at":"2018-02-24T11:21:15.000Z","updated_at":"2026-04-02T13:09:38.000Z","published_at":"2018-02-24T11:49:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a sum result\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e value of a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number of addends, build an array of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e elements\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that the following equality is satisfied:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum(y) = x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or [8 2].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore formally if x = a and N = n it results:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = [y_1 y_2 y_3 ... y_n] where: y_1 + y_2 + y_3 +...+ y_n = a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImportant notice: All the elements in y must be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edifferent from zero\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edifferent from each other\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . On the other hand I will not take into account if they are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegers or decimal numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck and enjoy with the solution ;)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42382,"title":"Combined Ages 1 - Symmetric, n = 3","description":"You have probably seen the common riddle wherein combined ages are provided and you must determine the individual ages. For example: If the ages of Alex and Barry sum to 43, the ages of Alex and Chris sum to 55, and the ages of Barry and Chris sum to 66, what are their individual ages?\r\n\r\nFor this problem, we'll assume that the three individuals are represented by A, B, and C, whereas the sums are AB, AC, and BC:\r\n\r\n* A+B = AB (= 43)\r\n* A+C = AC (= 55)\r\n* B+C = BC (= 66)\r\n\r\nAs you might have noticed, this is a simple matrix algebra problem. Write a function to return the individuals' ages [A;B;C] based on the supplied sums [AB AC BC].","description_html":"\u003cp\u003eYou have probably seen the common riddle wherein combined ages are provided and you must determine the individual ages. For example: If the ages of Alex and Barry sum to 43, the ages of Alex and Chris sum to 55, and the ages of Barry and Chris sum to 66, what are their individual ages?\u003c/p\u003e\u003cp\u003eFor this problem, we'll assume that the three individuals are represented by A, B, and C, whereas the sums are AB, AC, and BC:\u003c/p\u003e\u003cul\u003e\u003cli\u003eA+B = AB (= 43)\u003c/li\u003e\u003cli\u003eA+C = AC (= 55)\u003c/li\u003e\u003cli\u003eB+C = BC (= 66)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eAs you might have noticed, this is a simple matrix algebra problem. Write a function to return the individuals' ages [A;B;C] based on the supplied sums [AB AC BC].\u003c/p\u003e","function_template":"function y = combined_ages(AB,BC,AC)\r\n y = [1;1;1];\r\nend","test_suite":"%%\r\nAB = 43;\r\nBC = 55;\r\nAC = 66;\r\ny = combined_ages(AB,BC,AC);\r\ny_correct = [27 16 39];\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 30;\r\nBC = 50;\r\nAC = 40;\r\ny = combined_ages(AB,BC,AC);\r\ny_correct = [10 20 30];\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 20;\r\nBC = 70;\r\nAC = 60;\r\ny = combined_ages(AB,BC,AC);\r\ny_correct = [5 15 55];\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 34;\r\nBC = 84;\r\nAC = 56;\r\ny = combined_ages(AB,BC,AC);\r\ny_correct = [3 31 53];\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [2 11 21];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\ny = combined_ages(AB,BC,AC);\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [11 17 21];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\ny = combined_ages(AB,BC,AC);\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [15 35 55];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\ny = combined_ages(AB,BC,AC);\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":326,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-16T17:30:16.000Z","updated_at":"2026-03-29T20:59:40.000Z","published_at":"2015-06-16T17:30:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have probably seen the common riddle wherein combined ages are provided and you must determine the individual ages. For example: If the ages of Alex and Barry sum to 43, the ages of Alex and Chris sum to 55, and the ages of Barry and Chris sum to 66, what are their individual ages?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, we'll assume that the three individuals are represented by A, B, and C, whereas the sums are AB, AC, and BC:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+B = AB (= 43)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+C = AC (= 55)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eB+C = BC (= 66)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs you might have noticed, this is a simple matrix algebra problem. Write a function to return the individuals' ages [A;B;C] based on the supplied sums [AB AC BC].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":55700,"title":"Basic Mathematics 7","description":"Three generous robotics team mentors would jointly like to donate $N toward extra supplies. The second mentor is donating twice as much as the first mentor and dedicating their money towards PVC pipe.  The third mentor is donating $20 less than the second to wiring.  How much are you receiving from each mentor?\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThree generous robotics team mentors would jointly like to donate $N toward extra supplies. The second mentor is donating twice as much as the first mentor and dedicating their money towards PVC pipe.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe third mentor is donating $20 less than the second to wiring.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHow much are you receiving from each mentor?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [M1,M2,M3] = mentorDollars(N) % Do not edit this line.\r\n  % insert your code here\r\n  N = ?;\r\nend % Do not edit this line.\r\n\r\n","test_suite":"%%\r\n[M1, M2, M3] = mentorDollars(100);\r\nassert(isequal(M1,24), \"M1 donation is correct\");\r\nassert(isequal(M2,48), \"M2 donation is correct\");\r\nassert(isequal(M3,28), \"M3 donation is correct\");\r\n%% \r\n[M1, M2, M3] = mentorDollars(500);\r\nassert(isequal(M1,104), \"M1 donation is correct\");\r\nassert(isequal(M2,208), \"M2 donation is correct\");\r\nassert(isequal(M3,188), \"M3 donation is correct\");\r\n%% \r\n[M1, M2, M3] = mentorDollars(180);\r\nassert(isequal(M1,40), \"M1 donation is correct\");\r\nassert(isequal(M2,80), \"M2 donation is correct\");\r\nassert(isequal(M3,60), \"M3 donation is correct\");\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":542228,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":288,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T18:40:48.000Z","updated_at":"2026-03-30T16:40:07.000Z","published_at":"2022-09-13T18:40:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThree generous robotics team mentors would jointly like to donate $N toward extra supplies. The second mentor is donating twice as much as the first mentor and dedicating their money towards PVC pipe.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe third mentor is donating $20 less than the second to wiring.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eHow much are you receiving from each mentor?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":543,"title":"deconvolution","description":"* Suppose there is a vector v like [1 0 0 -1], representing polynomial coefficients.\r\n* In this example, the polynimial is 1*x^3+0*x^2+0*x-1 or (x^3-1).\r\n* Suppose there is another vector w like [1 -1].\r\n* In this example, the second polynomial is (x-1).\r\n* If x is any integer then the polynomial represented by (v/w) is integer?\r\n ","description_html":"\u003cul\u003e\u003cli\u003eSuppose there is a vector v like [1 0 0 -1], representing polynomial coefficients.\u003c/li\u003e\u003cli\u003eIn this example, the polynimial is 1*x^3+0*x^2+0*x-1 or (x^3-1).\u003c/li\u003e\u003cli\u003eSuppose there is another vector w like [1 -1].\u003c/li\u003e\u003cli\u003eIn this example, the second polynomial is (x-1).\u003c/li\u003e\u003cli\u003eIf x is any integer then the polynomial represented by (v/w) is integer?\u003c/li\u003e\u003c/ul\u003e","function_template":"function yesno = integ(v,w)\r\n  yesno=1==1/1; % yes\r\n  yesno=1==1/2; % no\r\nend","test_suite":"%%\r\nv=[1 0 0 -1];\r\nw=[1 -1];\r\nassert(integ(v,w))\r\n%%\r\nv=[2 9 6 -1 16 -5];\r\nw=[2 3 -1 5];\r\nassert(integ(v,w))\r\n%%\r\nv=[1 4 10 20 35 50 58 58 49 30];\r\nw=1:6;\r\nassert(integ(v,w))\r\n%%\r\nv=1:10;\r\nw=1:6;\r\nassert(~integ(v,w))\r\n%%\r\nv=3:12;\r\nw=-3:2;\r\nassert(~integ(v,w))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2012-03-31T22:38:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-31T22:38:54.000Z","updated_at":"2025-12-08T23:40:32.000Z","published_at":"2012-03-31T22:38:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose there is a vector v like [1 0 0 -1], representing polynomial coefficients.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this example, the polynimial is 1*x^3+0*x^2+0*x-1 or (x^3-1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose there is another vector w like [1 -1].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this example, the second polynomial is (x-1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf x is any integer then the polynomial represented by (v/w) is integer?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60979,"title":"Mesh the cube","description":"Problem statement : mesh the cube with quadranglar / squared faces\r\n\r\nAn cube / regular hexahedron is a regular polyhedron with 8 vertices and 6 squared / quadrangular faces. It is also one of the five well known platonic solids.\r\nA quadrangular mesh F (stands for faces here) is simply a N x 4 matrix of positive integers where each row contains the vertex indices of squared faces, and where N is the number of faces. \r\n\r\nYour task here is to mesh this cube. To do so, you will list the squares/rows in a matrix of faces, F. You will also be careful to always keep the faces coherently / consistently oriented (all clockwise or all counterclockwise : square [1, 2, 3, 4] and [4, 3, 2, 1] are distinct).\r\nOn the other hand [1, 2, 3, 4], [2, 3, 4, 1], [3, 4, 1, 2] and [4, 1, 2, 3] are one same unique square.\r\nThe row order of the faces in the list doesn't matter.\r\n\r\nEdit / update\r\nFaces orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\r\n\r\nExample\r\nThe first square (Z \u003e 0) here can be [1, 2, 3, 4] if counterclockwise oriented (normals outward).\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1194.73px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 597.367px; transform-origin: 408px 597.367px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 229.433px 8px; transform-origin: 229.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement : mesh the cube with quadranglar / squared faces\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.933px 8px; transform-origin: 376.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn cube / regular hexahedron is a regular polyhedron with 8 vertices and 6 squared / quadrangular faces. It is also one of the five well known platonic solids.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.8583px 8px; transform-origin: 68.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA quadrangular mesh \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eF\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.9417px 8px; transform-origin: 36.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.725px 8px; transform-origin: 16.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003efaces\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.8417px 8px; transform-origin: 54.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here) is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185.533px 8px; transform-origin: 185.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 4 matrix of positive integers where each row contains the vertex indices of squared faces, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.6667px 8px; transform-origin: 74.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of faces. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 296.108px 8px; transform-origin: 296.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this cube. To do so, you will list the squares/rows in a matrix of faces, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.25833px 8px; transform-origin: 7.25833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eF. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.6583px 8px; transform-origin: 80.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will also be careful to always keep the faces coherently / consistently oriented (all clockwise or all counterclockwise : square \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1px 8px; transform-origin: 31.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3, 4]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.4917px 8px; transform-origin: 17.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[4, 3, 2, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.0583px 8px; transform-origin: 40.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are distinct).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the other hand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1px 8px; transform-origin: 31.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3, 4]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 66.0833px 8px; transform-origin: 66.0833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[2, 3, 4, 1], [3, 4, 1, 2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1px 8px; transform-origin: 31.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[4, 1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.975px 8px; transform-origin: 92.975px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are one same unique square.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 158.842px 8px; transform-origin: 158.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the faces in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.9833px 8px; transform-origin: 41.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdit / update\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 342.275px 8px; transform-origin: 342.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFaces orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5583px 8px; transform-origin: 50.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first square \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.8083px 8px; transform-origin: 20.8083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(Z \u0026gt; 0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1583px 8px; transform-origin: 29.1583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3, 4]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148.208px 8px; transform-origin: 148.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented (normals outward).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 378px; font-family: Helvetica, 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function F = mesh_the_cube()\r\n  F = 1;\r\nend","test_suite":"%%\r\nF_correct = [1 2 3 4;\r\n             8 7 6 5;\r\n             1 4 8 5;\r\n             2 1 5 6;\r\n             3 2 6 7;\r\n             4 3 7 8];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_cube(),2)),sortrows(sort(F_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_cube.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:44:33.000Z","deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":"2025-07-23T16:15:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T10:23:00.000Z","updated_at":"2026-03-31T18:43:29.000Z","published_at":"2025-07-23T10:53:38.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement : mesh the cube with quadranglar / squared faces\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn cube / regular hexahedron is a regular polyhedron with 8 vertices and 6 squared / quadrangular faces. It is also one of the five well known platonic solids.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA quadrangular mesh \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (stands for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efaces\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here) is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 4 matrix of positive integers where each row contains the vertex indices of squared faces, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of faces. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh this cube. To do so, you will list the squares/rows in a matrix of faces, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eYou will also be careful to always keep the faces coherently / consistently oriented (all clockwise or all counterclockwise : square \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[4, 3, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are distinct).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[2, 3, 4, 1], [3, 4, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[4, 1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are one same unique square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe row order of the faces in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEdit / update\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFaces orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first square \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(Z \u0026gt; 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented (normals outward).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"378\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"504\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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The sum of twice the cans points plus three times the beach ball points, is N.\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365px 8px; transform-origin: 365px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt was announced during a Robotics Competition kick off that two of the trickiest scoring objects are: soup cans, and beach balls.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; 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transform-origin: 167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe sum of twice the cans points plus three times the beach ball points, is N.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function points[cans,balls] = findPoints(N) % Do not edit this line.\r\n  % insert your code here\r\n  cans = ?\r\n  balls = ?\r\nend % Do not edit this line.\r\n\r\n","test_suite":"%%\r\n[cans, balls] = findPoints(55)\r\nassert(isequal(cans,5), \"right number of cans\");\r\nassert(isequal(balls,15), \"right number of balls\");\r\n%%\r\n[cans, balls] = findPoints(75)\r\nassert(isequal(cans,9), \"right number of cans\");\r\nassert(isequal(balls,19), \"right number of balls\");\r\n%%\r\n[cans, balls] = findPoints(35)\r\nassert(isequal(cans,1), \"right number of cans\");\r\nassert(isequal(balls,11), \"right number of balls\");\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":542228,"edited_by":223089,"edited_at":"2022-10-14T07:06:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":264,"test_suite_updated_at":"2022-09-13T17:30:46.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T14:47:10.000Z","updated_at":"2026-03-30T16:31:13.000Z","published_at":"2022-09-13T14:47:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt was announced during a Robotics Competition kick off that two of the trickiest scoring objects are: soup cans, and beach balls.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe beach ball is worth ten more points than the cans.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe sum of twice the cans points plus three times the beach ball points, is N.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":463,"title":"Looking for Squares","description":"Need n squares that equal one square all together, none zero, none fractured. For example, calling squares(2) should output [16 9] or [25 144] etc, because 16=4*4, 9=3*3, and 16+9=5*5, similarly 25=5*5, 144=12*12, and 25+144=13*13.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373px 8px; transform-origin: 373px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNeed n squares that equal one square all together, none zero, none fractured. For example, calling squares(2) should output [16 9] or [25 144] etc, because 16=4*4, 9=3*3, and 16+9=5*5, similarly 25=5*5, 144=12*12, and 25+144=13*13.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function sq = squares(n)\r\n  sq=[1 4 25 144];\r\nend","test_suite":"%%\r\nfor n=3:7;\r\n   sq=squares(n);\r\n   assert(length(sq)==n)\r\n   for k=1:n\r\n      assert(sq(k)\u003e0)\r\n      assert(round(sqrt(sq(k)))==sqrt(sq(k)))\r\n   end\r\n   assert(round(sqrt(sum(sq)))==sqrt(sum(sq)))\r\nend\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":166,"edited_by":223089,"edited_at":"2023-02-21T05:30:33.000Z","deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2023-02-21T05:30:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-07T08:17:03.000Z","updated_at":"2025-05-16T15:38:29.000Z","published_at":"2012-03-07T08:25:05.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeed n squares that equal one square all together, none zero, none fractured. For example, calling squares(2) should output [16 9] or [25 144] etc, because 16=4*4, 9=3*3, and 16+9=5*5, similarly 25=5*5, 144=12*12, and 25+144=13*13.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60978,"title":"Mesh the octahedron","description":"Problem statement\r\n\r\nAn octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five well known platonic solids.\r\nA triangulated mesh -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this octahedron. To do so, you will list the triangles/rows in a matrix of triangles, T. You will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles [1, 2, 3] and [3, 2, 1] are distinct).\r\nOn the other hand [1, 2, 3], [2, 3, 1] and [3, 1, 2] are one same unique triangle.\r\nThe row order of the triangles in the list doesn't matter.\r\n\r\nEdit / update\r\nTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\r\n\r\nExample\r\nThe first triangle (X \u003e 0, Y \u003e 0, and Z \u003e 0) here can be [1, 2, 5] if counterclockwise oriented (normals are outward oriented).\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1200.23px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 600.117px; transform-origin: 408px 600.117px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373.817px 8px; transform-origin: 373.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five well known platonic solids.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.542px 8px; transform-origin: 157.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.533px 8px; transform-origin: 206.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 327.242px 8px; transform-origin: 327.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this octahedron. To do so, you will list the triangles/rows in a matrix of triangles, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.51667px 8px; transform-origin: 7.51667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.9333px 8px; transform-origin: 49.9333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 2, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.0583px 8px; transform-origin: 40.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are distinct).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the other hand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[2, 3, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 1, 2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5333px 8px; transform-origin: 94.5333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are one same unique triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.9833px 8px; transform-origin: 41.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdit / update\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 351.75px 8px; transform-origin: 351.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.1167px 8px; transform-origin: 52.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.2583px 8px; transform-origin: 75.2583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(X \u0026gt; 0, Y \u0026gt; 0, and Z \u0026gt; 0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 5]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 187.5px 8px; transform-origin: 187.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented (normals are outward oriented).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_octahedron()\r\n  T = 1;\r\nend","test_suite":"%%\r\nT_correct = [1 2 5;\r\n             2 3 5;\r\n             3 4 5;\r\n             4 1 5;\r\n             2 1 6;\r\n             3 2 6;\r\n             4 3 6;\r\n             1 4 6];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_octahedron(),2)),sortrows(sort(T_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_octahedron.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:44:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2025-07-23T16:11:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T08:24:47.000Z","updated_at":"2026-03-31T18:40:36.000Z","published_at":"2025-07-23T09:23:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five well known platonic solids.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh this octahedron. To do so, you will list the triangles/rows in a matrix of triangles, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are distinct).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[2, 3, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are one same unique triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEdit / update\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(X \u0026gt; 0, Y \u0026gt; 0, and Z \u0026gt; 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented (normals are outward oriented).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"378\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"504\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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all the three given point in the same line?","description":"In this problem the input is the coordinate of the three points in a XY plane?\r\n\r\nP1(X1,Y1)\r\n\r\nP2(X2,Y2)\r\n\r\nP3(X3,Y3)\r\n\r\nhow can we find out if all the three points are on the same line or not?\r\n\r\nfor example the points (1,1) , (-1,-1) , (0,0) are on the line y=x.","description_html":"\u003cp\u003eIn this problem the input is the coordinate of the three points in a XY plane?\u003c/p\u003e\u003cp\u003eP1(X1,Y1)\u003c/p\u003e\u003cp\u003eP2(X2,Y2)\u003c/p\u003e\u003cp\u003eP3(X3,Y3)\u003c/p\u003e\u003cp\u003ehow can we find out if all the three points are on the same line or not?\u003c/p\u003e\u003cp\u003efor example the points (1,1) , (-1,-1) , (0,0) are on the line y=x.\u003c/p\u003e","function_template":"% inputs are vectors;\r\n% X=[x1 x2 x3];\r\n% Y=[y1 y2 y3];\r\nfunction y = your_fcn_name(X,Y)\r\n  y = true;\r\nend","test_suite":"%%\r\nX = [-1 1 0];\r\nY=[-1 1 0];\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(X,Y),y_correct))\r\n\r\n%%\r\nX = [0 3 6];\r\nY=[5 7 9];\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(X,Y),y_correct))\r\n\r\n%%\r\nX = [0 7 14];\r\nY=[-7 -5 -3];\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(X,Y),y_correct))\r\n\r\n%%\r\nX = [10 12 -10];\r\nY=[-7 -3 47];\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(X,Y),y_correct))\r\n\r\n%%\r\nX = [0 0.8 1];\r\nY=[0.2 1 1];\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(X,Y),y_correct))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":1,"created_by":4320,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":603,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":17,"created_at":"2012-06-15T13:30:42.000Z","updated_at":"2026-03-13T04:50:21.000Z","published_at":"2012-06-15T13:30:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem the input is the coordinate of the three points in a XY plane?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP1(X1,Y1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP2(X2,Y2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP3(X3,Y3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehow can we find out if all the three points are on the same line or not?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efor example the points (1,1) , (-1,-1) , (0,0) are on the line y=x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":57447,"title":"Compute a nested cube root","description":"Consider the quantity . Write a function to compute  without using loops or recursion. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.075px 8px; transform-origin: 68.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the quantity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\" style=\"width: 249px; height: 19.5px;\" width=\"249\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.875px 8px; transform-origin: 90.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Write a function to compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71.575px 8px; transform-origin: 71.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e without using loops or recursion. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = nestedCubeRoot(a)\r\n  y = nthroot(a+nthroot(a+nthroot(a+nthroot(a,3),3),3),3);\r\nend","test_suite":"%%\r\na = 6;\r\nassert(abs(nestedCubeRoot(a)-2)\u003c1e-14)\r\n\r\n%%\r\na = 24;\r\nassert(abs(nestedCubeRoot(a)-3)\u003c1e-14)\r\n\r\n%%\r\na = 120;\r\nassert(abs(nestedCubeRoot(a)-5)\u003c1e-14)\r\n\r\n%%\r\na = 336;\r\nassert(abs(nestedCubeRoot(a)-7)\u003c1e-14)\r\n\r\n%%\r\na = 1320;\r\nassert(abs(nestedCubeRoot(a)-11)\u003c1e-14)\r\n\r\n%%\r\na = 15/8;\r\nassert(abs(nestedCubeRoot(a)-3/2)\u003c1e-14)\r\n\r\n%%\r\na = 2040/2197;\r\nassert(abs(nestedCubeRoot(a)-17/13)\u003c1e-14)\r\n\r\n%%\r\na = 9048/12167;\r\nassert(abs(nestedCubeRoot(a)-29/23)\u003c1e-14)\r\n\r\n%%\r\na = 29520/29791;\r\nassert(abs(nestedCubeRoot(a)-41/31)\u003c1e-14)\r\n\r\n%%\r\na = 117384/226981;\r\nassert(abs(nestedCubeRoot(a)-73/61)\u003c1e-14)\r\n\r\n%%\r\na = 2259912/3869893;\r\nassert(abs(nestedCubeRoot(a)-191/157)\u003c1e-14)\r\n\r\n%%\r\nfiletext = fileread('nestedCubeRoot.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'switch') || contains(filetext,'for') || contains(filetext,'while') || length(strfind(filetext,'nestedCubeRoot')) \u003e 1;\r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-21T13:18:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-21T13:13:13.000Z","updated_at":"2026-03-04T12:08:30.000Z","published_at":"2022-12-21T13:18:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the quantity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = (a+(a+(a+(a+\\\\ldots)^{1/3})^{1/3})^{1/3})^{1/3}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Write a function to compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e without using loops or recursion. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42384,"title":"Combined Ages 2 - Symmetric, n ≥ 3","description":"Following on \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42382-combined-ages-1-symmetric-n-3 Combined Ages 2\u003e, you will now be provided with age sums for _n_ individuals where _n_ ≥ 3. The sums will be provided in sorted order and will be for _n–1_ individuals (e.g., A+B+C, A+B+D, A+C+D, B+C+D). See the previous problem for an explanation, the test suite for examples, and the problem tags for hints.","description_html":"\u003cp\u003eFollowing on \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42382-combined-ages-1-symmetric-n-3\"\u003eCombined Ages 2\u003c/a\u003e, you will now be provided with age sums for \u003ci\u003en\u003c/i\u003e individuals where \u003ci\u003en\u003c/i\u003e ≥ 3. The sums will be provided in sorted order and will be for \u003ci\u003en–1\u003c/i\u003e individuals (e.g., A+B+C, A+B+D, A+C+D, B+C+D). See the previous problem for an explanation, the test suite for examples, and the problem tags for hints.\u003c/p\u003e","function_template":"function y = combined_ages2(varargin)\r\n y = ones(nargin,1);\r\nend","test_suite":"%%\r\nAB = 43;\r\nAC = 66;\r\nBC = 55;\r\ny = combined_ages2(AB,AC,BC);\r\ny_correct = [27 16 39];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 30;\r\nAC = 40;\r\nBC = 50;\r\ny = combined_ages2(AB,AC,BC);\r\ny_correct = [10 20 30];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABC = 72;\r\nABD = 66;\r\nACD = 70;\r\nBCD = 77;\r\ny = combined_ages2(ABC,ABD,ACD,BCD);\r\ny_correct = [18 25 29 23];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABC = 66;\r\nABD = 67;\r\nACD = 68;\r\nBCD = 69;\r\ny = combined_ages2(ABC,ABD,ACD,BCD);\r\ny_correct = [21 22 23 24];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABC = 60;\r\nABD = 65;\r\nACD = 70;\r\nBCD = 75;\r\ny = combined_ages2(ABC,ABD,ACD,BCD);\r\ny_correct = [15 20 25 30];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCD = 90;\r\nABCE = 115;\r\nABDE = 100;\r\nACDE = 110;\r\nBCDE = 105;\r\ny = combined_ages2(ABCD,ABCE,ABDE,ACDE,BCDE);\r\ny_correct = [25 20 30 15 40];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCD = 44;\r\nABCE = 37;\r\nABDE = 47;\r\nACDE = 51;\r\nBCDE = 53;\r\ny = combined_ages2(ABCD,ABCE,ABDE,ACDE,BCDE);\r\ny_correct = [5 7 11 21 14];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCDEF = 133;\r\nABCDEG = 186;\r\nABCDFG = 172;\r\nABCEFG = 163;\r\nABDEFG = 192;\r\nACDEFG = 200;\r\nBCDEFG = 184;\r\ny = combined_ages2(ABCDEF,ABCDEG,ABCDFG,ABCEFG,ABDEFG,ACDEFG,BCDEFG);\r\ny_correct = [21 5 13 42 33 19 72];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":183,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-16T19:13:14.000Z","updated_at":"2026-03-29T21:29:20.000Z","published_at":"2015-06-16T19:13:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollowing on\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42382-combined-ages-1-symmetric-n-3\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCombined Ages 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, you will now be provided with age sums for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e individuals where\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 3. The sums will be provided in sorted order and will be for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en–1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e individuals (e.g., A+B+C, A+B+D, A+C+D, B+C+D). See the previous problem for an explanation, the test suite for examples, and the problem tags for hints.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42385,"title":"Combined Ages 4 - Non-symmetric with multiples, n ≥ 3","description":"This problem is slightly more difficult than \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42383-combined-ages-3-non-symmetric-n-3 Combined Ages 3\u003e. In this case, some of the sums may include multiples of some individuals' ages. As an example: If the ages of all three individuals with Chris's age added again sum to 98, the ages of Barry (twice) and Chris sum to 84, and the ages of Alex (twice) and Barry sum to 70, what are their individual ages?\r\n\r\nThe individuals will be represented by the first n capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:\r\n\r\n* A+B+C+C = ABCC (= 98)\r\n* B+B+C = BBC (= 84)\r\n* A+A+B = AAB (= 70)\r\n\r\nThough the variables are ordered above, they will not always be in the test cases. Write a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.","description_html":"\u003cp\u003eThis problem is slightly more difficult than \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42383-combined-ages-3-non-symmetric-n-3\"\u003eCombined Ages 3\u003c/a\u003e. In this case, some of the sums may include multiples of some individuals' ages. As an example: If the ages of all three individuals with Chris's age added again sum to 98, the ages of Barry (twice) and Chris sum to 84, and the ages of Alex (twice) and Barry sum to 70, what are their individual ages?\u003c/p\u003e\u003cp\u003eThe individuals will be represented by the first n capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:\u003c/p\u003e\u003cul\u003e\u003cli\u003eA+B+C+C = ABCC (= 98)\u003c/li\u003e\u003cli\u003eB+B+C = BBC (= 84)\u003c/li\u003e\u003cli\u003eA+A+B = AAB (= 70)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThough the variables are ordered above, they will not always be in the test cases. Write a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.\u003c/p\u003e","function_template":"function y = combined_ages_nonsymmetric_w_mult(varargin)\r\n y = ones(nargin,1);\r\nend","test_suite":"%%\r\nABCD = 70;\r\nABC = 65;\r\nAB = 40;\r\nBC = 52;\r\ny = combined_ages_nonsymmetric_w_mult(ABCD,ABC,AB,BC);\r\ny_correct = [13;27;25;5];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCC = 98;\r\nBBC = 84;\r\nAAB = 70;\r\ny = combined_ages_nonsymmetric_w_mult(ABCC,BBC,AAB);\r\ny_correct = [20;30;24];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCDA = 150;\r\nABCB = 99;\r\nBCDB = 91;\r\nABDAD = 135;\r\ny = combined_ages_nonsymmetric_w_mult(ABCDA,ABCB,BCDB,ABDAD);\r\ny_correct = [35;11;42;27];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABBA = 90;\r\nBCC = 113;\r\nABCBA = 141;\r\ny = combined_ages_nonsymmetric_w_mult(ABBA,BCC,ABCBA);\r\ny_correct = [34;11;51];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCDE = 120;\r\nABCDD = 111;\r\nABCCC = 87;\r\nABBBB = 66;\r\nAAAAA = 50;\r\ny = combined_ages_nonsymmetric_w_mult(ABCDE,ABCDD,ABCCC,ABBBB,AAAAA);\r\ny_correct = [10,14,21,33,42];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABC = 45;\r\nBEA = 66;\r\nCAE = 73;\r\nDAB = 57;\r\nAAD = 53;\r\ny = combined_ages_nonsymmetric_w_mult(ABC,BEA,CAE,DAB,AAD);\r\ny_correct = [10,14,21,33,42];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCABC = 144;\r\nBEAB = 107;\r\nCAEAD = 147;\r\nDABB = 73;\r\nAADAA = 133;\r\ny = combined_ages_nonsymmetric_w_mult(ABCABC,BEAB,CAEAD,DABB,AADAA);\r\ny_correct = [30,15,27,13,47];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%% anti-cheating test case\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tABCC = 98;\r\n\t\tBBC = 84;\r\n\t\tAAB = 70;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCC,BBC,AAB);\r\n\t\ty_correct = [20;30;24];\r\n\tcase 2\r\n\t\tABCDA = 150;\r\n\t\tABCB = 99;\r\n\t\tBCDB = 91;\r\n\t\tABDAD = 135;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCDA,ABCB,BCDB,ABDAD);\r\n\t\ty_correct = [35;11;42;27];\r\n\tcase 3\r\n\t\tABCABC = 144;\r\n\t\tBEAB = 107;\r\n\t\tCAEAD = 147;\r\n\t\tDABB = 73;\r\n\t\tAADAA = 133;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCABC,BEAB,CAEAD,DABB,AADAA);\r\n\t\ty_correct = [30,15,27,13,47];\r\n\tcase 4\r\n\t\tABCD = 70;\r\n\t\tABC = 65;\r\n\t\tAB = 40;\r\n\t\tBC = 52;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCD,ABC,AB,BC);\r\n\t\ty_correct = [13;27;25;5];\r\nend\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%% anti-cheating test case\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tABCC = 98;\r\n\t\tBBC = 84;\r\n\t\tAAB = 70;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCC,BBC,AAB);\r\n\t\ty_correct = [20;30;24];\r\n\tcase 2\r\n\t\tABCABC = 144;\r\n\t\tBEAB = 107;\r\n\t\tCAEAD = 147;\r\n\t\tDABB = 73;\r\n\t\tAADAA = 133;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCABC,BEAB,CAEAD,DABB,AADAA);\r\n\t\ty_correct = [30,15,27,13,47];\r\n\tcase 3\r\n\t\tABCD = 70;\r\n\t\tABC = 65;\r\n\t\tAB = 40;\r\n\t\tBC = 52;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCD,ABC,AB,BC);\r\n\t\ty_correct = [13;27;25;5];\r\n\tcase 4\r\n\t\tABC = 45;\r\n\t\tBEA = 66;\r\n\t\tCAE = 73;\r\n\t\tDAB = 57;\r\n\t\tAAD = 53;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABC,BEA,CAE,DAB,AAD);\r\n\t\ty_correct = [10,14,21,33,42];\r\nend\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%% anti-cheating test case\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tABBA = 90;\r\n\t\tBCC = 113;\r\n\t\tABCBA = 141;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABBA,BCC,ABCBA);\r\n\t\ty_correct = [34;11;51];\r\n\tcase 2\r\n\t\tABCD = 70;\r\n\t\tABC = 65;\r\n\t\tAB = 40;\r\n\t\tBC = 52;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCD,ABC,AB,BC);\r\n\t\ty_correct = [13;27;25;5];\r\n\tcase 3\r\n\t\tABCDA = 150;\r\n\t\tABCB = 99;\r\n\t\tBCDB = 91;\r\n\t\tABDAD = 135;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCDA,ABCB,BCDB,ABDAD);\r\n\t\ty_correct = [35;11;42;27];\r\n\tcase 4\r\n\t\tABCC = 98;\r\n\t\tBBC = 84;\r\n\t\tAAB = 70;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCC,BBC,AAB);\r\n\t\ty_correct = [20;30;24];\r\nend\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":122,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-16T20:03:26.000Z","updated_at":"2026-03-24T04:49:54.000Z","published_at":"2015-06-16T20:03:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is slightly more difficult than\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42383-combined-ages-3-non-symmetric-n-3\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCombined Ages 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. In this case, some of the sums may include multiples of some individuals' ages. As an example: If the ages of all three individuals with Chris's age added again sum to 98, the ages of Barry (twice) and Chris sum to 84, and the ages of Alex (twice) and Barry sum to 70, what are their individual ages?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe individuals will be represented by the first n capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+B+C+C = ABCC (= 98)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eB+B+C = BBC (= 84)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+A+B = AAB (= 70)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThough the variables are ordered above, they will not always be in the test cases. Write a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42383,"title":"Combined Ages 3 - Non-symmetric, n ≥ 3","description":"Pursuant to the previous two problems ( \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42382-combined-ages-1-symmetric-n-3 Symmetric, n = 3\u003e and \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42384-combined-ages-2-symmetric-n-3 Symmetric, n ≥ 3\u003e ), this problem will provide _n_ combined ages where _n_ is the number of individuals, though the age sums will not form a symmetric matrix. As an example: If the ages of all four individuals sum to 70; the ages of Alex, Barry, and Chris sum to 65; the ages of Alex and Barry sum to 40; and the ages of Barry and Chris sum to 52, what are their individual ages?\r\n\r\nThe individuals will be represented by the first _n_ capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:\r\n\r\n* A+B+C+D = ABCD (= 70)\r\n* A+B+C = ABC (= 65)\r\n* A+B = AB (= 40)\r\n* B+C = BC (= 52)\r\n\r\nWrite a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.","description_html":"\u003cp\u003ePursuant to the previous two problems ( \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42382-combined-ages-1-symmetric-n-3\"\u003eSymmetric, n = 3\u003c/a\u003e and \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42384-combined-ages-2-symmetric-n-3\"\u003eSymmetric, n ≥ 3\u003c/a\u003e ), this problem will provide \u003ci\u003en\u003c/i\u003e combined ages where \u003ci\u003en\u003c/i\u003e is the number of individuals, though the age sums will not form a symmetric matrix. As an example: If the ages of all four individuals sum to 70; the ages of Alex, Barry, and Chris sum to 65; the ages of Alex and Barry sum to 40; and the ages of Barry and Chris sum to 52, what are their individual ages?\u003c/p\u003e\u003cp\u003eThe individuals will be represented by the first \u003ci\u003en\u003c/i\u003e capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:\u003c/p\u003e\u003cul\u003e\u003cli\u003eA+B+C+D = ABCD (= 70)\u003c/li\u003e\u003cli\u003eA+B+C = ABC (= 65)\u003c/li\u003e\u003cli\u003eA+B = AB (= 40)\u003c/li\u003e\u003cli\u003eB+C = BC (= 52)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eWrite a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.\u003c/p\u003e","function_template":"function y = combined_ages_nonsymmetric(varargin)\r\n y = ones(nargin,1);\r\nend","test_suite":"%%\r\nABCD = 70;\r\nABC = 65;\r\nAB = 40;\r\nBC = 52;\r\ny = combined_ages_nonsymmetric(ABCD,ABC,AB,BC);\r\ny_correct = [13;27;25;5];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABC = 70;\r\nBC = 50;\r\nAC = 40;\r\ny = combined_ages_nonsymmetric(ABC,BC,AC);\r\ny_correct = [20;30;20];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCD = 100;\r\nABC = 80;\r\nBCD = 70;\r\nABD = 60;\r\ny = combined_ages_nonsymmetric(ABCD,ABC,BCD,ABD);\r\ny_correct = [30;10;40;20];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 34;\r\nBC = 54;\r\nABC = 86;\r\ny = combined_ages_nonsymmetric(AB,BC,ABC);\r\ny_correct = [32;2;52];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCDE = 120;\r\nABCD = 78;\r\nABC = 45;\r\nAB = 24;\r\nAC = 31;\r\ny = combined_ages_nonsymmetric(ABCDE,ABCD,ABC,AB,AC);\r\ny_correct = [10,14,21,33,42];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [37 33 31 38];\r\nABC = y_correct(1) + y_correct(2) + y_correct(3);\r\nBCD = y_correct(2) + y_correct(3) + y_correct(4);\r\nACD = y_correct(1) + y_correct(3) + y_correct(4);\r\nABD = y_correct(1) + y_correct(2) + y_correct(4);\r\ny = combined_ages_nonsymmetric(ABC,BCD,ACD,ABD);\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [5 15 30 62 100];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\nACE = y_correct(1) + y_correct(3) + y_correct(5);\r\nABDE = y_correct(1) + y_correct(2) + y_correct(4) + y_correct(5);\r\ny = combined_ages_nonsymmetric(AB,BC,AC,ACE,ABDE);\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [2 3 5 7 11 17 23 31 42 55];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\nABCD = y_correct(1) + y_correct(2) + y_correct(3) + y_correct(4);\r\nCDEG = y_correct(3) + y_correct(4) + y_correct(5) + y_correct(7);\r\nBFH = y_correct(2) + y_correct(6) + y_correct(8);\r\nFGIJ = y_correct(6) + y_correct(7) + y_correct(9) + y_correct(10);\r\nACEGH = y_correct(1) + y_correct(3) + y_correct(5) + y_correct(7) + y_correct(8);\r\nBEJ = y_correct(2) + y_correct(5) + y_correct(10);\r\nABDIJ = y_correct(1) + y_correct(2) + y_correct(4) + y_correct(9) + y_correct(10);\r\ny = combined_ages_nonsymmetric(AB,BC,AC,ABCD,CDEG,BFH,FGIJ,ACEGH,BEJ,ABDIJ);\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%% anti-cheating test case\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tABCD = 70;\r\n\t\tABC = 65;\r\n\t\tAB = 40;\r\n\t\tBC = 52;\r\n\t\ty = combined_ages_nonsymmetric(ABCD,ABC,AB,BC);\r\n\t\ty_correct = [13;27;25;5];\r\n\tcase 2\r\n\t\tABCD = 100;\r\n\t\tABC = 80;\r\n\t\tBCD = 70;\r\n\t\tABD = 60;\r\n\t\ty = combined_ages_nonsymmetric(ABCD,ABC,BCD,ABD);\r\n\t\ty_correct = [30;10;40;20];\r\n\tcase 3\r\n\t\tAB = 34;\r\n\t\tBC = 54;\r\n\t\tABC = 86;\r\n\t\ty = combined_ages_nonsymmetric(AB,BC,ABC);\r\n\t\ty_correct = [32;2;52];\r\n\tcase 4\r\n\t\tABC = 70;\r\n\t\tBC = 50;\r\n\t\tAC = 40;\r\n\t\ty = combined_ages_nonsymmetric(ABC,BC,AC);\r\n\t\ty_correct = [20;30;20];\r\nend\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%% anti-cheating test case\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tABC = 70;\r\n\t\tBC = 50;\r\n\t\tAC = 40;\r\n\t\ty = combined_ages_nonsymmetric(ABC,BC,AC);\r\n\t\ty_correct = [20;30;20];\r\n\tcase 2\r\n\t\tAB = 34;\r\n\t\tBC = 54;\r\n\t\tABC = 86;\r\n\t\ty = combined_ages_nonsymmetric(AB,BC,ABC);\r\n\t\ty_correct = [32;2;52];\r\n\tcase 3\r\n\t\tABCD = 70;\r\n\t\tABC = 65;\r\n\t\tAB = 40;\r\n\t\tBC = 52;\r\n\t\ty = combined_ages_nonsymmetric(ABCD,ABC,AB,BC);\r\n\t\ty_correct = [13;27;25;5];\r\n\tcase 4\r\n\t\tABCD = 100;\r\n\t\tABC = 80;\r\n\t\tBCD = 70;\r\n\t\tABD = 60;\r\n\t\ty = combined_ages_nonsymmetric(ABCD,ABC,BCD,ABD);\r\n\t\ty_correct = [30;10;40;20];\r\nend\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%% anti-cheating test case\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tAB = 34;\r\n\t\tBC = 54;\r\n\t\tABC = 86;\r\n\t\ty = combined_ages_nonsymmetric(AB,BC,ABC);\r\n\t\ty_correct = [32;2;52];\r\n\tcase 2\r\n\t\tABCD = 100;\r\n\t\tABC = 80;\r\n\t\tBCD = 70;\r\n\t\tABD = 60;\r\n\t\ty = combined_ages_nonsymmetric(ABCD,ABC,BCD,ABD);\r\n\t\ty_correct = [30;10;40;20];\r\n\tcase 3\r\n\t\tABCD = 70;\r\n\t\tABC = 65;\r\n\t\tAB = 40;\r\n\t\tBC = 52;\r\n\t\ty = combined_ages_nonsymmetric(ABCD,ABC,AB,BC);\r\n\t\ty_correct = [13;27;25;5];\r\n\tcase 4\r\n\t\tABC = 70;\r\n\t\tBC = 50;\r\n\t\tAC = 40;\r\n\t\ty = combined_ages_nonsymmetric(ABC,BC,AC);\r\n\t\ty_correct = [20;30;20];\r\nend\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":144,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-16T18:34:18.000Z","updated_at":"2026-03-29T22:25:18.000Z","published_at":"2015-06-16T18:34:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePursuant to the previous two problems (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42382-combined-ages-1-symmetric-n-3\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSymmetric, n = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42384-combined-ages-2-symmetric-n-3\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSymmetric, n ≥ 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ), this problem will provide\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e combined ages where\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of individuals, though the age sums will not form a symmetric matrix. As an example: If the ages of all four individuals sum to 70; the ages of Alex, Barry, and Chris sum to 65; the ages of Alex and Barry sum to 40; and the ages of Barry and Chris sum to 52, what are their individual ages?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe individuals will be represented by the first\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+B+C+D = ABCD (= 70)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+B+C = ABC (= 65)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+B = AB (= 40)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eB+C = BC (= 52)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52861,"title":"Easy Sequences 37: Natural Factorable Polynomials","description":"A polynomial of the form: , for , is said to be natural factorable if it can be factored into products of first degree binomials: , where,  and  are all natural numbers (i.e. integers that are ).\r\nGiven an integer , write a function that counts the number of all possible natural factorable polynomials that can be formed, wherein .\r\nFor example, when , the are  possible natural factorable polynomials, namely:\r\n                                    ;\r\n                                    ;\r\n                                    ;\r\n                                    ;\r\n                                    \r\n                                    ; and\r\n                                    \r\nTherefore the function output should be .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 384px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA polynomial of the form: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"287.5\" height=\"21\" style=\"width: 287.5px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, is said to be natural factorable if it can be factored into products of first degree binomials: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"214.5\" height=\"20\" style=\"width: 214.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, where, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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width=\"140\" height=\"20\" style=\"width: 140px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"131.5\" height=\"20\" style=\"width: 131.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eall\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e natural numbers (i.e. integers that are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"25\" height=\"18\" style=\"width: 25px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, write a function that counts the number of all possible natural factorable polynomials that can be formed, wherein \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIcAAAAoCAYAAADUrekxAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAh6ADAAQAAAABAAAAKAAAAAAoS6xrAAAFkklEQVR4Ae2Ya6hVRRTHzfJWkj3oQRZqmJlaqGSBH6oPlVlSQYpB9OASomEPtIio8IY96EJlPoIywk9qD3pgHyoIopdmkiVh9aHIm5hZVJZWlpn1+9dZ3LnTPvucfffMOed2Z8GPee5Zs9ZeM3tmDxiQJHkgeSB5IHkgeSB5IHkgeSB5IHkgeaCve+AkDFgEx/R1Q9L8w3lgGEMth73wF4yCJP3cAydi/6PwOygojBQcOKMJMhWdMxqpd2COsqW07YRZsC+nX2qK54EDGPoy2ACvwmRoOdnMjFph5xjEPCa0nHfCT0iLdiZsAvO70vnQcrKeGdkkm/FZORj9c+FL2Aj/VzkQw66CT8D8rfQlmAQtKc0KjsF4Q6tlO5iz3m9JD5WblHbE6+AzMDuVroEzoClyUFO01lY6hC43wC1wbKW7DsZPQmelXCZp42F9y8eDAvB5+BYuhxNgIfwEsUU7ooLidhjhKFNQaA4fOnUhslHsbtTOcSQe6IAfwFbQb+SXgW5PIUQn/q9hP7wFL8AusHOVdGt7jykKyHnwFZidmo/mMhFiSDS7YweHfqzdD1qt5qw95JeAVnIouY2B9BK+g/HOoHeSN73POfWhs4cxoHaJb8D0aT7auWIetKPaHSs4jscpD8HPYM5SUCyGoRBSHmMw6dgNZ3kDX1tpU/scry1UcS4DfQ9mp1IFohukFINLdLtDB4f+uupToUAwZ/1K/hEIHRQM+c8NwPRcowpPOilb+8leW6jilQz0haNH+t6G8yGW6OZjdkWzO1RwDGeyT4AOlzZpBcUi0C4SQ3SO2QHS9ynoH4Ivr1Ch9i1+Q+CyLgDapTQPs1/pO3ABhJSG2R0qOKZjvXuukGNeg1NDesUb63HK9iK0en05nIofQX1W+I2UR8OD8DLotnQ16M9lGVGAzoRNYHNTuhYuhBBS1u665xAqOKRQEd0B7vf3T8qrYAyElKMZ7A+Q47dC1q6xoNKuPlrVrkyloJ3NfYHKK4iyxqK6kCjILgXXvxp/HUh3b6Ws3YX0upMfVejJ6p11ctcpegeY8xUkq2EshJB2BrGxn84Y8Ajqdjp9hjl9DiW/DbRraPfQz6jFYOOdQz6k6LPyBtj4St+Fi6CotPOAjVPU7qK6ekR2qOCwSegl3ARa2WaQguQpGAdlRDchG1M/1Hx5gApr7/IaL6H8jFenopytZ+5WIYKczZh2BrK5rafu4gK6ythdQM2/Xd8jsYmGDg6bTBuZWfC5o0tBohd0GvRG9Kmyefvb9BW06Vpr7SsrCq4nPRfOA+0YvtxKhZ7JCja/b5nyJB5+EfaDzXFBnQOWsbtOFd3dusjaBE/vro6S099JHfo+BtMpBz0LRXXf5Ywxn7zJNDJ7QM42HTeS17+I7TAcqoluW3pmYrUOgetl82rQQtEnrh6JYfd/9OpFzQNzoNKHYRDEFh3WZsAHYPoVJMugXtE5wZ7dS34N6NahcWSXtnBr12dtF5wJeaJr6EdQ9saSpyOr7RQqJ2Q1ZNTFsLuHmk5K7p9Lc6JSXUc39+gdt6CVvg6ke2MBVXqB94ICw+a/hfx0kIwEq9eOMVmVOaJPzW4Yk9OnFZqC2N3o6C/rOL2cKXBHwYG06nRu6QJ9rnS9NRlLZijoXPWLVWakR1G3ARaCnU8yulWt0m9y3Y7KyDYeVnDXKyHsrldXv+3XhuWvwz0lPPAmz9ou1du03jNHiWl2PzqwO5tyVTygc9cq0Ge0w+tziFfOK7q7VV6/vLZ9eY2h2/raZyW0/bXGk39WgBZRO2jFm8wmcxzcZxU10iG0D67Rp1azDsy6ZTVEUnDku3kJzTfDWnBXrYJiNIyErZCkn3lgDvbmnQ10JU6SPJA8kDyQPJA8kDyQPJA8kDyQPJA8kDyQPJA80Doe+BtrbtjTY15rYgAAAABJRU5ErkJggg==\" width=\"67.5\" height=\"20\" style=\"width: 67.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, when \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, the are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e7\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e possible natural factorable polynomials, namely:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"212.5\" height=\"20\" style=\"width: 212.5px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore the function output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e7\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = numPols(a)\r\n  y = x;\r\nend","test_suite":"%%\r\na = 4;\r\nn_correct = 7;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\na = 5;\r\nn_correct = 13;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\na = 10;\r\nn_correct = 128;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\na = 20;\r\nn_correct = 2693;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\na = 50;\r\nn_correct = 1295920;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\nas = 51:150;\r\nns = arrayfun(@(a) numPols(a),as);\r\nss = int64([sum(ns) ns(1:20:end) floor(std(ns))])\r\nss_correct = [4267039260053 1535862 34751087 529784816 6145056743 58130508732 88934830907];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\na = 75;\r\nn_correct = 61537319;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\na = 100;\r\nn_correct = 1642992467;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\na = 150;\r\nn_correct = 423652454768;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\nfiletext = fileread('numPols.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-06T10:42:04.000Z","updated_at":"2026-02-24T17:43:19.000Z","published_at":"2021-10-07T11:06:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA polynomial of the form: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^n+a_2x^{n-1}+a_3x^{n-2}+...+a_{n-2}x^2+a_{n-1}x+a_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026gt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is said to be natural factorable if it can be factored into products of first degree binomials: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x+r_1)(x+r_2)...(x+r_{n-1})(x+r_n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_2,\\\\ a_3,\\\\ a_4,\\\\ ...\\\\ a_{n-1},\\\\ a_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_1,\\\\ r_2,\\\\ r_3,\\\\ ...\\\\ r_{n-1},\\\\ r_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eall\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e natural numbers (i.e. integers that are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ge1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a function that counts the number of all possible natural factorable polynomials that can be formed, wherein \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \u0026lt; a_2\\\\le a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, when \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e possible natural factorable polynomials, namely:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^2+2x+1=(x+1)^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^2+3x+2=(x+1)(x+2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^2+4x+3 = (x+1)(x+3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^2+4x+4 = (x+2)^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^3+3x^2+3x+1=(x+1)^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^3+4x^2+5x+2 = (x+1)^2(x+2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^4+4x^3+6x^2+4x+1=(x+1)^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore the function output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":43296,"title":"Refresh your system of equations","description":"Given square matrix, and solution vector, find the values of the variables\r\n\r\nExample:\r\n\r\nxyz = [1 -1 2; 0 2 5; 4 0 -3]; //x-y+2z; 2y+5x; 4x-3z\r\nabc = [21; 21; 21]\r\ny_correct =  [ 9 -2 5 ];","description_html":"\u003cp\u003eGiven square matrix, and solution vector, find the values of the variables\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003exyz = [1 -1 2; 0 2 5; 4 0 -3]; //x-y+2z; 2y+5x; 4x-3z\r\nabc = [21; 21; 21]\r\ny_correct =  [ 9 -2 5 ];\u003c/p\u003e","function_template":"function y = answerMe(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nxyz = [1 -1 2; 0 2 5; 4 0 -3];\r\nabc = [21; 21; 21];\r\ny_correct =  [ 9 -2 5 ];\r\nassert(sum((transpose(answerMe(xyz,abc))-y_correct))\u003c0.01)\r\n%%\r\nxyz = [1 2; 1 -2];\r\nabc = [3; -1];\r\ny_correct =  [ 1 1];\r\nassert(isequal(nnz(answerMe(xyz,abc)-y_correct),0))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":3,"created_by":13865,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":53,"test_suite_updated_at":"2016-10-29T16:24:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-10T07:22:44.000Z","updated_at":"2026-02-12T11:59:59.000Z","published_at":"2016-10-10T07:22:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven square matrix, and solution vector, find the values of the variables\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003exyz = [1 -1 2; 0 2 5; 4 0 -3]; //x-y+2z; 2y+5x; 4x-3z abc = [21; 21; 21] y_correct = [ 9 -2 5 ];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2971,"title":"square a vector-Given the variable x as your input, square it and put the result in y.","description":"function y = (x)squared\r\n \r\n y = x;\r\nend","description_html":"\u003cp\u003efunction y = (x)squared\u003c/p\u003e\u003cpre\u003e y = x;\r\nend\u003c/pre\u003e","function_template":"function y = (x)squared\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal((x)^2,y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":33779,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":112,"test_suite_updated_at":"2015-02-07T00:41:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-02-07T00:34:32.000Z","updated_at":"2026-02-19T14:25:21.000Z","published_at":"2015-02-07T00:36:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efunction y = (x)squared\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = x;\\nend]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45430,"title":"Juego de posiciones","description":"Crea una función que ordene vectores de tal manera que los primeros números sean negativos ordenados de menor a mayor. Y después vayan los números positivos ordenados de mayor a menor. \r\n\r\nPor ejemplo:\r\n\r\ny = [-1 6 15 -7 31 2 -4 -5];\r\n\r\ny_correct = [-7 -5 -4 -1 31 15 6 2];\r\n\r\nPD: Considerad el cero como número positivo. ","description_html":"\u003cp\u003eCrea una función que ordene vectores de tal manera que los primeros números sean negativos ordenados de menor a mayor. Y después vayan los números positivos ordenados de mayor a menor.\u003c/p\u003e\u003cp\u003ePor ejemplo:\u003c/p\u003e\u003cp\u003ey = [-1 6 15 -7 31 2 -4 -5];\u003c/p\u003e\u003cp\u003ey_correct = [-7 -5 -4 -1 31 15 6 2];\u003c/p\u003e\u003cp\u003ePD: Considerad el cero como número positivo.\u003c/p\u003e","function_template":"function x = order(y)\r\n \r\nend","test_suite":"%%\r\ny = [-1 6 15 -7 31 2 -4 -5];\r\ny_correct = [-7 -5 -4 -1 31 15 6 2];\r\nassert(isequal(order(y),y_correct))\r\n%%\r\ny=[6 7 -34 9 0];\r\ny_correct= [-34 9 7 6 0];\r\nassert(isequal(order(y),y_correct))\r\n%%\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":394942,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-09T11:48:17.000Z","updated_at":"2026-03-02T14:14:33.000Z","published_at":"2020-04-10T07:53:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCrea una función que ordene vectores de tal manera que los primeros números sean negativos ordenados de menor a mayor. Y después vayan los números positivos ordenados de mayor a menor.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePor ejemplo:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = [-1 6 15 -7 31 2 -4 -5];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_correct = [-7 -5 -4 -1 31 15 6 2];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePD: Considerad el cero como número positivo.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42986,"title":"Determine the roots of a cubic equation","description":"Given the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.","description_html":"\u003cp\u003eGiven the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.\u003c/p\u003e","function_template":"function y = cubicRoots(a,b,c,d)\r\n  y = [0 0 0];\r\nend","test_suite":"%%\r\na=1; b=3; c=3; d=1;\r\ny_correct = [-1 -1 -1];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)\r\n\r\n%%\r\na=1; b=-6; c=11; d=-6;\r\ny_correct = [1 2 3];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)\r\n\r\n%%\r\na=4; b=4; c=-1; d=-1;\r\ny_correct = [-1 -0.5 0.5];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":91311,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":"2016-09-30T16:42:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-09-16T10:40:42.000Z","updated_at":"2026-03-11T08:50:39.000Z","published_at":"2016-09-16T10:40:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60982,"title":"Mesh the square with triangles","description":"Problem statement\r\n\r\nAn square is a regular polygon with 4 vertices and 4 edges.\r\nA triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh, that is to say give one triangulation T of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\r\n\r\nExample\r\nThe first triangle here can be [1, 2, 3] if counterclockwise oriented.\r\n\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 995.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 497.617px; transform-origin: 408px 497.617px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.608px 8px; transform-origin: 183.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.983px 8px; transform-origin: 176.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.633px 8px; transform-origin: 132.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.275px 8px; transform-origin: 192.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh, that is to say give one triangulation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.583px 8px; transform-origin: 183.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.8583px 8px; transform-origin: 89.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 340.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 170.25px; text-align: left; transform-origin: 385px 170.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"447\" height=\"335\" style=\"vertical-align: baseline;width: 447px;height: 335px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_square()\r\n  T = 1;\r\nend","test_suite":"%% Test every possible solutions\r\nT_correct1 = [1 2 3;\r\n              3 4 1];\r\n\r\nT_correct2 = [2 3 4;\r\n              1 2 4];\r\n\r\nassert(isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct1,2)))...\r\n     | isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct2,2))))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_square.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:45:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T16:29:27.000Z","updated_at":"2026-02-10T17:10:21.000Z","published_at":"2025-07-23T16:40:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh, that is to say give one triangulation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId 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Are you more familiar with iteration methods or Linear Algebra ? Let's see together.","description":"Referring to problem:\r\n\r\nhttps://www.mathworks.com/matlabcentral/cody/problems/44530-are-you-more-familiar-with-iteration-methods-or-linear-algebra-let-s-see-together\r\n\r\nGiven a sum result *_x_* value of a *_N_* number of addends, build an array of _*N*_ elements _*y*_ such that the following equality is satisfied: _sum(y) = x_ .\r\n\r\nFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].\r\n\r\nMore formally if x = a and N = n it results: \r\n\r\ny = [y_1 y_2 y_3 ... y_n]\r\nwhere:  y_1 + y_2 + y_3 +...+ y_n = a\r\n\r\nImportant notice: All the elements in y must be: *different from zero*, *different from each other* and *strictly positive* . On the other hand I will not take into account if they are _integers or decimal numbers_ .\r\n\r\nHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\r\n\r\nGood luck and enjoy with the solution ;)","description_html":"\u003cp\u003eReferring to problem:\u003c/p\u003e\u003cp\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/44530-are-you-more-familiar-with-iteration-methods-or-linear-algebra-let-s-see-together\u003c/p\u003e\u003cp\u003eGiven a sum result \u003cb\u003e\u003ci\u003ex\u003c/i\u003e\u003c/b\u003e value of a \u003cb\u003e\u003ci\u003eN\u003c/i\u003e\u003c/b\u003e number of addends, build an array of \u003ci\u003e\u003cb\u003eN\u003c/b\u003e\u003c/i\u003e elements \u003ci\u003e\u003cb\u003ey\u003c/b\u003e\u003c/i\u003e such that the following equality is satisfied: \u003ci\u003esum(y) = x\u003c/i\u003e .\u003c/p\u003e\u003cp\u003eFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].\u003c/p\u003e\u003cp\u003eMore formally if x = a and N = n it results:\u003c/p\u003e\u003cp\u003ey = [y_1 y_2 y_3 ... y_n]\r\nwhere:  y_1 + y_2 + y_3 +...+ y_n = a\u003c/p\u003e\u003cp\u003eImportant notice: All the elements in y must be: \u003cb\u003edifferent from zero\u003c/b\u003e, \u003cb\u003edifferent from each other\u003c/b\u003e and \u003cb\u003estrictly positive\u003c/b\u003e . On the other hand I will not take into account if they are \u003ci\u003eintegers or decimal numbers\u003c/i\u003e .\u003c/p\u003e\u003cp\u003eHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\u003c/p\u003e\u003cp\u003eGood luck and enjoy with the solution ;)\u003c/p\u003e","function_template":"function y = buildSumArray(x,N);\r\n  y = sum(1:N);\r\nend","test_suite":"%% Test Case 1\r\nx = 6;\r\nN = 3;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\nassert(isempty(y(y \u003c 0)))\r\n\r\n%% Test Case 2\r\nx = 13;\r\nN = 5;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\nassert(isempty(y(y \u003c 0)))\r\n\r\n%% Test Case 3\r\nx = 78;\r\nN = 11;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\nassert(isempty(y(y \u003c 0)))\r\n\r\n%% Test Case 4\r\nx = 2689;\r\nN = 245;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\nassert(isempty(y(y \u003c 0)))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":181340,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":677,"created_at":"2018-02-24T14:17:32.000Z","updated_at":"2026-03-05T10:42:37.000Z","published_at":"2018-02-24T14:18:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReferring to problem:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44530-are-you-more-familiar-with-iteration-methods-or-linear-algebra-let-s-see-together\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/44530-are-you-more-familiar-with-iteration-methods-or-linear-algebra-let-s-see-together\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a sum result\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e value of a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number of addends, build an array of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e elements\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that the following equality is satisfied:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum(y) = x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or [8 2].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore formally if x = a and N = n it results:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = [y_1 y_2 y_3 ... y_n] where: y_1 + y_2 + y_3 +...+ y_n = a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImportant notice: All the elements in y must be:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edifferent from zero\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edifferent from each other\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estrictly positive\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . On the other hand I will not take into account if they are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegers or decimal numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck and enjoy with the solution ;)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60306,"title":"Add non-triangular numbers","description":"The nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems 5, 291, 44289, 44334, 44732, 55680, 55695, 55705, 55710, and 55715, for example. \r\nWrite a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.658px 8px; transform-origin: 377.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/5\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e5\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/291\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e291\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44289\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44289\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44334\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44334\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44732\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44732\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55680\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55680\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55695\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55695\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55705\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55705\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55710\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55710\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.775px 8px; transform-origin: 16.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55715\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55715\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, for example. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 362.975px 8px; transform-origin: 362.975px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = addNonTriangular(n)\r\n  y = sum(tril(n)+1:triu(n)-1);\r\nend","test_suite":"%%\r\nassert(isequal(addNonTriangular(1),2))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(2),9))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(3),24))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(4),50))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(44),44550))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(92),397854))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(267),9588504))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(389),29583450))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(461),49198842))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(556),86249222))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(632),126617724))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(709),178703450))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(878),339189399))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(913),381358274))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(1255),989903840))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(6534),139521237075))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(14342),1475229944979))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(78422),241154195453019))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(256347),8422831459859544))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(addNonTriangular(2429)/(3^10*347)),21560175))\r\n\r\n%%\r\ns = [0 1 4 9 6 5 6 9 4 1];\r\nn = randi(1000);\r\nm = n:n+2;\r\nd = num2str((2*arrayfun(@addNonTriangular,m)./m)')-'0';\r\nd1 = d(:,end)';\r\nassert(~isempty(strfind([s s],d1)))\r\n\r\n%%\r\nfiletext = fileread('addNonTriangular.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'sum') || contains(filetext,'trace')  || contains(filetext,'ones')  || contains(filetext,'eye'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-14T01:38:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-14T01:37:57.000Z","updated_at":"2026-03-04T14:14:54.000Z","published_at":"2024-05-14T01:38:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/5\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/291\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e291\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44289\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44289\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44334\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44334\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44732\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44732\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55680\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55680\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55695\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55695\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55705\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55705\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55710\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55710\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55715\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55715\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, for example. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60980,"title":"Mesh the tetrahedron","description":"Problem statement\r\n\r\nAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\r\nA triangulated mesh -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, T. You will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles [1, 2, 3] and [3, 2, 1] are distinct).\r\nOn the other hand [1, 2, 3], [2, 3, 1] and [3, 1, 2] are one same unique triangle.\r\nThe row order of the triangles in the list doesn't matter.\r\n       \r\nEdit / update\r\nTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\r\n\r\nExample\r\nThe first triangle (X \u003e 0 and Y \u003e 0) here can be [1, 2, 4] if counterclockwise oriented (normals outward).\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1194.73px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 597.367px; transform-origin: 408px 597.367px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.592px 8px; transform-origin: 374.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.542px 8px; transform-origin: 157.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.533px 8px; transform-origin: 206.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 328.017px 8px; transform-origin: 328.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.51667px 8px; transform-origin: 7.51667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.4667px 8px; transform-origin: 49.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 2, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.0583px 8px; transform-origin: 40.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are distinct).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the other hand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[2, 3, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 1, 2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5333px 8px; transform-origin: 94.5333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are one same unique triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.5917px 8px; transform-origin: 13.5917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e       \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.9833px 8px; transform-origin: 41.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdit / update\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 351.75px 8px; transform-origin: 351.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.1167px 8px; transform-origin: 52.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.2917px 8px; transform-origin: 53.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(X \u0026gt; 0 and Y \u0026gt; 0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 4]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148.208px 8px; transform-origin: 148.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented (normals outward).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 378px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 189px; text-align: left; transform-origin: 385px 189px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"504\" height=\"378\" style=\"vertical-align: middle;width: 504px;height: 378px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_tetrahedron()\r\n  T = 1;\r\nend","test_suite":"%%\r\nT_correct = [1 2 4;\r\n             2 3 4;\r\n             3 1 4;\r\n             1 3 2];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_tetrahedron(),2)),sortrows(sort(T_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_tetrahedron.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:43:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":"2025-07-23T16:17:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T11:03:01.000Z","updated_at":"2026-03-31T18:44:34.000Z","published_at":"2025-07-23T11:11:01.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are distinct).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[2, 3, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are one same unique triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEdit / update\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(X \u0026gt; 0 and Y \u0026gt; 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented (normals outward).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"378\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"504\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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Sequences 23: Hat Guessing Game!","description":"Consider the following Game Show:\r\nHats, with numbers written on each, were placed on the heads of the participants. Participants can see the numbers on all hats, except their own. Each participant were asked to add all the numbers they do see and write the sum on a piece of paper card. The participants were then asked to hide their hats and show only their cards with numbers, to you, the contestant. For a prize of a million dollars, you were asked to guess the numbers written on each participant's hat.\r\nAssuming that all sums are correct, will you be the next millionare? Let's find out...","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 144px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the following Game Show:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eHats, with numbers written on each, were placed on the heads of the participants. Participants can see the numbers on all hats, except their own. Each participant were asked to add all the numbers they do see and write the sum on a piece of paper card. The participants were then asked to hide their hats and show only their cards with numbers, to you, the contestant. For a prize of a million dollars, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eyou were asked to guess the numbers written on each participant's hat.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eAssuming that all sums are correct, will you be the next millionare? Let's find out...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function nums = hatNumbers(sums)\r\n    nums = sums;\r\nend","test_suite":"%%\r\nsums = [667 658 645 688 629 625 713 630 637 678];\r\nnums_correct = [63 72 85 42 101 105 17 100 93 52];\r\nassert(isequal(hatNumbers(sums),nums_correct))\r\n%%\r\nsums = [1460 1459 1394 1416 1411 1428 1439 1394 1393 1395 1471 1470 ...\r\n        1469 1468 1395 1408 1407 1408 1395 1384 1439 1428 1406 1395 1460];\r\nnums_correct = [23 24 89 67 72 55 44 89 90 88 12 13 14 15 88 75 76 75 88 99 44 55 77 88 23];\r\nassert(isequal(hatNumbers(sums),nums_correct))\r\n%%\r\nsums = [ ...\r\n4892 4927 4901 4949 4896 4963 4939 4962 4957 4884 4897 4935 4871 4963 4923 4928 4890 4887 4948 4918 ...\r\n4922 4902 4896 4891 4939 4899 4901 4950 4955 4917 4871 4932 4908 4944 4891 4941 4916 4897 4877 4871 ...\r\n4912 4953 4952 4941 4882 4941 4885 4942 4874 4932 4947 4941 4905 4919 4931 4883 4908 4912 4875 4938 ...\r\n4891 4891 4928 4910 4959 4961 4913 4889 4873 4954 4910 4920 4965 4933 4950 4887 4935 4914 4950 4906 ...\r\n4940 4901 4898 4892 4921 4958 4944 4875 4951 4884 4913 4867 4959 4922 4956 4870 4966 4889 4885 4880 ...\r\n];\r\nnums = hatNumbers(sums);\r\nnums_stats = round([std(nums) mean(nums) mode(nums) median(nums)],4);\r\nassert(isequal(nums_stats,[28.8090 49.6700 26.0000 50.5000]))\r\n%%\r\nnums = randi(1000,1,1000).*97+2;\r\nsums = arrayfun(@(n) sum(nums(n-1:-1:1))+sum(nums(n+1:end)), 1:length(nums));\r\nassert(isequal(hatNumbers(sums),nums))\r\n%%\r\nfiletext = fileread('hatNumbers.m');\r\nblocked = {'solve' 'fsolve' 'dsolve' 'linsolve' 'mldivide' 'mrdivide' '\\' '/'};\r\nnot_allowed = any(arrayfun(@(s) contains(filetext, blocked{s}), 1:8));\r\nassert(~not_allowed)\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2021-09-24T08:03:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-22T11:19:54.000Z","updated_at":"2025-12-07T16:32:52.000Z","published_at":"2021-09-24T08:03:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the following Game Show:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHats, with numbers written on each, were placed on the heads of the participants. Participants can see the numbers on all hats, except their own. Each participant were asked to add all the numbers they do see and write the sum on a piece of paper card. The participants were then asked to hide their hats and show only their cards with numbers, to you, the contestant. For a prize of a million dollars, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eyou were asked to guess the numbers written on each participant's hat.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssuming that all sums are correct, will you be the next millionare? Let's find out...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60981,"title":"Mesh the pentagon (with the minimum number of triangles)","description":"Problem statement\r\n\r\nAn pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set V, corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.\r\n\r\nV = [1           0            0;\r\n     cos(2*pi/5) sin(2*pi/5)  0;\r\n     cos(4*pi/5) sin(4*pi/5)  0;\r\n     cos(4*pi/5) sin(-4*pi/5) 0;\r\n     cos(2*pi/5) sin(-2*pi/5) 0];\r\n\r\nA triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, F. The row order of the triangles in the list doesn't matter.\r\n\r\nExample\r\nThe first triangle here can be [1, 2, 3] if counterclockwise oriented.\r\n\r\n\r\n\r\n\r\nTip\r\nBeware to avoid self intersecting triangles.\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1278.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 639.2px; transform-origin: 408px 639.2px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 327.525px 8px; transform-origin: 327.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.09167px 8px; transform-origin: 6.09167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2417px 8px; transform-origin: 48.2417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 51.0833px; transform-origin: 405px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eV = [1           0            0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(2*pi/5) sin(2*pi/5)  0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(4*pi/5) sin(4*pi/5)  0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(4*pi/5) sin(-4*pi/5) 0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 127.05px 8.5px; tab-size: 4; transform-origin: 127.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(2*pi/5) sin(-2*pi/5) 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.983px 8px; transform-origin: 176.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.633px 8px; transform-origin: 132.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384.442px 8px; transform-origin: 384.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.25833px 8px; transform-origin: 7.25833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eF. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.8583px 8px; transform-origin: 89.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 339.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 169.75px; text-align: left; transform-origin: 385px 169.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"445\" height=\"334\" style=\"vertical-align: baseline;width: 445px;height: 334px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.3667px 8px; transform-origin: 10.3667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTip\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 131.092px 8px; transform-origin: 131.092px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBeware to avoid self intersecting triangles.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_pentagon()\r\n  T = 1;\r\nend","test_suite":"%%\r\nT_correct1 = [1 2 3;\r\n              1 3 4;\r\n              1 4 5];\r\n\r\nT_correct2 = [2 3 4;\r\n              2 4 5;\r\n              2 5 1];\r\n\r\nT_correct3 = [3 4 5;\r\n              3 5 1;\r\n              3 1 2];\r\n\r\nT_correct4 = [3 4 5;\r\n              3 5 1;\r\n              3 1 2];\r\n\r\nT_correct5 = [5 1 2;\r\n              5 2 3;\r\n              5 3 4];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct1,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct2,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct3,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct4,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct5,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_pentagon.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":149128,"edited_by":149128,"edited_at":"2025-08-13T05:29:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":"2025-08-13T05:29:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T12:59:46.000Z","updated_at":"2026-02-10T17:07:57.000Z","published_at":"2025-07-23T15:54:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[V = [1           0            0;\\n     cos(2*pi/5) sin(2*pi/5)  0;\\n     cos(4*pi/5) sin(4*pi/5)  0;\\n     cos(4*pi/5) sin(-4*pi/5) 0;\\n     cos(2*pi/5) sin(-2*pi/5) 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"334\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"445\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTip\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBeware to avoid self intersecting triangles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/57483\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh 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Mathematics 4","description":"Team #1 is in first place but only one point higher than Team #2.  The sum of their two scores is N. What are each team’s scores?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTeam #1 is in first place but only one point higher than Team #2.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe sum of their two scores is N. What are each team’s scores?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [team1, team2] = teamPoints(N) % Do not edit this line.\r\n  % insert your code here\r\n  team1 = ?;\r\n  team2=?;\r\nend % Do not edit this line.\r\n","test_suite":"%%\r\n[team1, team2] = teamPoints(147);\r\nassert(isequal(team1,74),\"team1 points correct\");\r\nassert(isequal(team2,73), \"team2 points correct\");\r\n%%\r\n \r\n[team1, team2] = teamPoints(285);\r\nassert(isequal(team1,143), \"team1 points correct\");\r\nassert(isequal(team2,142), \"team2 points correct\");\r\n%%\r\n \r\n[team1, team2] = teamPoints(91);\r\nassert(isequal(team1,46), \"team1 points correct\");\r\nassert(isequal(team2,45), \"team2 points correct\");\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":542228,"edited_by":542228,"edited_at":"2022-09-13T17:29:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":363,"test_suite_updated_at":"2022-09-13T17:29:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T15:38:54.000Z","updated_at":"2026-03-30T16:36:17.000Z","published_at":"2022-09-13T15:38:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTeam #1 is in first place but only one point higher than Team #2.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe sum of their two scores is N. What are each team’s scores?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44530,"title":"Are you more familiar with iteration methods or Linear Algebra? Let's see together.","description":"Given a sum result *_x_* value of a *_N_* number of addends, build an array of _*N*_ elements _*y*_ such that the following equality is satisfied: _sum(y) = x_ .\r\n\r\nFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].\r\n\r\nMore formally if x = a and N = n it results: \r\n\r\ny = [y_1 y_2 y_3 ... y_n]\r\nwhere:  y_1 + y_2 + y_3 +...+ y_n = a\r\n\r\nImportant notice: All the elements in y must be *different from zero* and *different from each other* . On the other hand I will not take into account if they are _integers or decimal numbers_ .\r\n\r\nHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\r\n\r\nGood luck and enjoy with the solution ;)\r\n","description_html":"\u003cp\u003eGiven a sum result \u003cb\u003e\u003ci\u003ex\u003c/i\u003e\u003c/b\u003e value of a \u003cb\u003e\u003ci\u003eN\u003c/i\u003e\u003c/b\u003e number of addends, build an array of \u003ci\u003e\u003cb\u003eN\u003c/b\u003e\u003c/i\u003e elements \u003ci\u003e\u003cb\u003ey\u003c/b\u003e\u003c/i\u003e such that the following equality is satisfied: \u003ci\u003esum(y) = x\u003c/i\u003e .\u003c/p\u003e\u003cp\u003eFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].\u003c/p\u003e\u003cp\u003eMore formally if x = a and N = n it results:\u003c/p\u003e\u003cp\u003ey = [y_1 y_2 y_3 ... y_n]\r\nwhere:  y_1 + y_2 + y_3 +...+ y_n = a\u003c/p\u003e\u003cp\u003eImportant notice: All the elements in y must be \u003cb\u003edifferent from zero\u003c/b\u003e and \u003cb\u003edifferent from each other\u003c/b\u003e . On the other hand I will not take into account if they are \u003ci\u003eintegers or decimal numbers\u003c/i\u003e .\u003c/p\u003e\u003cp\u003eHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\u003c/p\u003e\u003cp\u003eGood luck and enjoy with the solution ;)\u003c/p\u003e","function_template":"function y = buildSumArray(x,N)\r\n  y = sum(1:N);\r\nend","test_suite":"%% Test Case 1\r\nx = 6;\r\nN = 3;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n\r\n%% Test Case 2\r\nx = 13;\r\nN = 5;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n\r\n\r\n%% Test Case 3\r\nx = 78;\r\nN = 11;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n\r\n\r\n%% Test Case 4\r\nx = 2689;\r\nN = 245;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":181340,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2018-02-24T12:07:13.000Z","rescore_all_solutions":false,"group_id":677,"created_at":"2018-02-24T11:21:15.000Z","updated_at":"2026-04-02T13:09:38.000Z","published_at":"2018-02-24T11:49:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a sum result\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e value of a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number of addends, build an array of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e elements\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that the following equality is satisfied:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum(y) = x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or [8 2].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore formally if x = a and N = n it results:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = [y_1 y_2 y_3 ... y_n] where: y_1 + y_2 + y_3 +...+ y_n = a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImportant notice: All the elements in y must be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edifferent from zero\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edifferent from each other\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . On the other hand I will not take into account if they are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegers or decimal numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck and enjoy with the solution ;)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42382,"title":"Combined Ages 1 - Symmetric, n = 3","description":"You have probably seen the common riddle wherein combined ages are provided and you must determine the individual ages. For example: If the ages of Alex and Barry sum to 43, the ages of Alex and Chris sum to 55, and the ages of Barry and Chris sum to 66, what are their individual ages?\r\n\r\nFor this problem, we'll assume that the three individuals are represented by A, B, and C, whereas the sums are AB, AC, and BC:\r\n\r\n* A+B = AB (= 43)\r\n* A+C = AC (= 55)\r\n* B+C = BC (= 66)\r\n\r\nAs you might have noticed, this is a simple matrix algebra problem. Write a function to return the individuals' ages [A;B;C] based on the supplied sums [AB AC BC].","description_html":"\u003cp\u003eYou have probably seen the common riddle wherein combined ages are provided and you must determine the individual ages. For example: If the ages of Alex and Barry sum to 43, the ages of Alex and Chris sum to 55, and the ages of Barry and Chris sum to 66, what are their individual ages?\u003c/p\u003e\u003cp\u003eFor this problem, we'll assume that the three individuals are represented by A, B, and C, whereas the sums are AB, AC, and BC:\u003c/p\u003e\u003cul\u003e\u003cli\u003eA+B = AB (= 43)\u003c/li\u003e\u003cli\u003eA+C = AC (= 55)\u003c/li\u003e\u003cli\u003eB+C = BC (= 66)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eAs you might have noticed, this is a simple matrix algebra problem. Write a function to return the individuals' ages [A;B;C] based on the supplied sums [AB AC BC].\u003c/p\u003e","function_template":"function y = combined_ages(AB,BC,AC)\r\n y = [1;1;1];\r\nend","test_suite":"%%\r\nAB = 43;\r\nBC = 55;\r\nAC = 66;\r\ny = combined_ages(AB,BC,AC);\r\ny_correct = [27 16 39];\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 30;\r\nBC = 50;\r\nAC = 40;\r\ny = combined_ages(AB,BC,AC);\r\ny_correct = [10 20 30];\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 20;\r\nBC = 70;\r\nAC = 60;\r\ny = combined_ages(AB,BC,AC);\r\ny_correct = [5 15 55];\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 34;\r\nBC = 84;\r\nAC = 56;\r\ny = combined_ages(AB,BC,AC);\r\ny_correct = [3 31 53];\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [2 11 21];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\ny = combined_ages(AB,BC,AC);\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [11 17 21];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\ny = combined_ages(AB,BC,AC);\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [15 35 55];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\ny = combined_ages(AB,BC,AC);\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":326,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-16T17:30:16.000Z","updated_at":"2026-03-29T20:59:40.000Z","published_at":"2015-06-16T17:30:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have probably seen the common riddle wherein combined ages are provided and you must determine the individual ages. For example: If the ages of Alex and Barry sum to 43, the ages of Alex and Chris sum to 55, and the ages of Barry and Chris sum to 66, what are their individual ages?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, we'll assume that the three individuals are represented by A, B, and C, whereas the sums are AB, AC, and BC:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+B = AB (= 43)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+C = AC (= 55)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eB+C = BC (= 66)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs you might have noticed, this is a simple matrix algebra problem. Write a function to return the individuals' ages [A;B;C] based on the supplied sums [AB AC BC].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":55700,"title":"Basic Mathematics 7","description":"Three generous robotics team mentors would jointly like to donate $N toward extra supplies. The second mentor is donating twice as much as the first mentor and dedicating their money towards PVC pipe.  The third mentor is donating $20 less than the second to wiring.  How much are you receiving from each mentor?\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThree generous robotics team mentors would jointly like to donate $N toward extra supplies. The second mentor is donating twice as much as the first mentor and dedicating their money towards PVC pipe.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe third mentor is donating $20 less than the second to wiring.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHow much are you receiving from each mentor?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [M1,M2,M3] = mentorDollars(N) % Do not edit this line.\r\n  % insert your code here\r\n  N = ?;\r\nend % Do not edit this line.\r\n\r\n","test_suite":"%%\r\n[M1, M2, M3] = mentorDollars(100);\r\nassert(isequal(M1,24), \"M1 donation is correct\");\r\nassert(isequal(M2,48), \"M2 donation is correct\");\r\nassert(isequal(M3,28), \"M3 donation is correct\");\r\n%% \r\n[M1, M2, M3] = mentorDollars(500);\r\nassert(isequal(M1,104), \"M1 donation is correct\");\r\nassert(isequal(M2,208), \"M2 donation is correct\");\r\nassert(isequal(M3,188), \"M3 donation is correct\");\r\n%% \r\n[M1, M2, M3] = mentorDollars(180);\r\nassert(isequal(M1,40), \"M1 donation is correct\");\r\nassert(isequal(M2,80), \"M2 donation is correct\");\r\nassert(isequal(M3,60), \"M3 donation is correct\");\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":542228,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":288,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T18:40:48.000Z","updated_at":"2026-03-30T16:40:07.000Z","published_at":"2022-09-13T18:40:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThree generous robotics team mentors would jointly like to donate $N toward extra supplies. The second mentor is donating twice as much as the first mentor and dedicating their money towards PVC pipe.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe third mentor is donating $20 less than the second to wiring.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eHow much are you receiving from each mentor?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":543,"title":"deconvolution","description":"* Suppose there is a vector v like [1 0 0 -1], representing polynomial coefficients.\r\n* In this example, the polynimial is 1*x^3+0*x^2+0*x-1 or (x^3-1).\r\n* Suppose there is another vector w like [1 -1].\r\n* In this example, the second polynomial is (x-1).\r\n* If x is any integer then the polynomial represented by (v/w) is integer?\r\n ","description_html":"\u003cul\u003e\u003cli\u003eSuppose there is a vector v like [1 0 0 -1], representing polynomial coefficients.\u003c/li\u003e\u003cli\u003eIn this example, the polynimial is 1*x^3+0*x^2+0*x-1 or (x^3-1).\u003c/li\u003e\u003cli\u003eSuppose there is another vector w like [1 -1].\u003c/li\u003e\u003cli\u003eIn this example, the second polynomial is (x-1).\u003c/li\u003e\u003cli\u003eIf x is any integer then the polynomial represented by (v/w) is integer?\u003c/li\u003e\u003c/ul\u003e","function_template":"function yesno = integ(v,w)\r\n  yesno=1==1/1; % yes\r\n  yesno=1==1/2; % no\r\nend","test_suite":"%%\r\nv=[1 0 0 -1];\r\nw=[1 -1];\r\nassert(integ(v,w))\r\n%%\r\nv=[2 9 6 -1 16 -5];\r\nw=[2 3 -1 5];\r\nassert(integ(v,w))\r\n%%\r\nv=[1 4 10 20 35 50 58 58 49 30];\r\nw=1:6;\r\nassert(integ(v,w))\r\n%%\r\nv=1:10;\r\nw=1:6;\r\nassert(~integ(v,w))\r\n%%\r\nv=3:12;\r\nw=-3:2;\r\nassert(~integ(v,w))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2012-03-31T22:38:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-31T22:38:54.000Z","updated_at":"2025-12-08T23:40:32.000Z","published_at":"2012-03-31T22:38:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose there is a vector v like [1 0 0 -1], representing polynomial coefficients.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this example, the polynimial is 1*x^3+0*x^2+0*x-1 or (x^3-1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose there is another vector w like [1 -1].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this example, the second polynomial is (x-1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf x is any integer then the polynomial represented by (v/w) is integer?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60979,"title":"Mesh the cube","description":"Problem statement : mesh the cube with quadranglar / squared faces\r\n\r\nAn cube / regular hexahedron is a regular polyhedron with 8 vertices and 6 squared / quadrangular faces. It is also one of the five well known platonic solids.\r\nA quadrangular mesh F (stands for faces here) is simply a N x 4 matrix of positive integers where each row contains the vertex indices of squared faces, and where N is the number of faces. \r\n\r\nYour task here is to mesh this cube. To do so, you will list the squares/rows in a matrix of faces, F. You will also be careful to always keep the faces coherently / consistently oriented (all clockwise or all counterclockwise : square [1, 2, 3, 4] and [4, 3, 2, 1] are distinct).\r\nOn the other hand [1, 2, 3, 4], [2, 3, 4, 1], [3, 4, 1, 2] and [4, 1, 2, 3] are one same unique square.\r\nThe row order of the faces in the list doesn't matter.\r\n\r\nEdit / update\r\nFaces orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\r\n\r\nExample\r\nThe first square (Z \u003e 0) here can be [1, 2, 3, 4] if counterclockwise oriented (normals outward).\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1194.73px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 597.367px; transform-origin: 408px 597.367px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 229.433px 8px; transform-origin: 229.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement : mesh the cube with quadranglar / squared faces\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.933px 8px; transform-origin: 376.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn cube / regular hexahedron is a regular polyhedron with 8 vertices and 6 squared / quadrangular faces. It is also one of the five well known platonic solids.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.8583px 8px; transform-origin: 68.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA quadrangular mesh \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eF\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.9417px 8px; transform-origin: 36.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.725px 8px; transform-origin: 16.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003efaces\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.8417px 8px; transform-origin: 54.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here) is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185.533px 8px; transform-origin: 185.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 4 matrix of positive integers where each row contains the vertex indices of squared faces, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.6667px 8px; transform-origin: 74.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of faces. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 296.108px 8px; transform-origin: 296.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this cube. To do so, you will list the squares/rows in a matrix of faces, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.25833px 8px; transform-origin: 7.25833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eF. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.6583px 8px; transform-origin: 80.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will also be careful to always keep the faces coherently / consistently oriented (all clockwise or all counterclockwise : square \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1px 8px; transform-origin: 31.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3, 4]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.4917px 8px; transform-origin: 17.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[4, 3, 2, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.0583px 8px; transform-origin: 40.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are distinct).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the other hand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1px 8px; transform-origin: 31.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3, 4]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 66.0833px 8px; transform-origin: 66.0833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[2, 3, 4, 1], [3, 4, 1, 2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1px 8px; transform-origin: 31.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[4, 1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.975px 8px; transform-origin: 92.975px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are one same unique square.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 158.842px 8px; transform-origin: 158.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the faces in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.9833px 8px; transform-origin: 41.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdit / update\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 342.275px 8px; transform-origin: 342.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFaces orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5583px 8px; transform-origin: 50.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first square \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.8083px 8px; transform-origin: 20.8083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(Z \u0026gt; 0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1583px 8px; transform-origin: 29.1583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3, 4]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148.208px 8px; transform-origin: 148.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented (normals outward).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 378px; font-family: Helvetica, 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function F = mesh_the_cube()\r\n  F = 1;\r\nend","test_suite":"%%\r\nF_correct = [1 2 3 4;\r\n             8 7 6 5;\r\n             1 4 8 5;\r\n             2 1 5 6;\r\n             3 2 6 7;\r\n             4 3 7 8];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_cube(),2)),sortrows(sort(F_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_cube.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:44:33.000Z","deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":"2025-07-23T16:15:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T10:23:00.000Z","updated_at":"2026-03-31T18:43:29.000Z","published_at":"2025-07-23T10:53:38.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement : mesh the cube with quadranglar / squared faces\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn cube / regular hexahedron is a regular polyhedron with 8 vertices and 6 squared / quadrangular faces. It is also one of the five well known platonic solids.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA quadrangular mesh \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (stands for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efaces\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here) is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 4 matrix of positive integers where each row contains the vertex indices of squared faces, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of faces. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh this cube. To do so, you will list the squares/rows in a matrix of faces, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eYou will also be careful to always keep the faces coherently / consistently oriented (all clockwise or all counterclockwise : square \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[4, 3, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are distinct).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[2, 3, 4, 1], [3, 4, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[4, 1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are one same unique square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe row order of the faces in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEdit / update\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFaces orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first square \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(Z \u0026gt; 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented (normals outward).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"378\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"504\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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The sum of twice the cans points plus three times the beach ball points, is N.\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365px 8px; transform-origin: 365px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt was announced during a Robotics Competition kick off that two of the trickiest scoring objects are: soup cans, and beach balls.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; 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transform-origin: 167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe sum of twice the cans points plus three times the beach ball points, is N.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function points[cans,balls] = findPoints(N) % Do not edit this line.\r\n  % insert your code here\r\n  cans = ?\r\n  balls = ?\r\nend % Do not edit this line.\r\n\r\n","test_suite":"%%\r\n[cans, balls] = findPoints(55)\r\nassert(isequal(cans,5), \"right number of cans\");\r\nassert(isequal(balls,15), \"right number of balls\");\r\n%%\r\n[cans, balls] = findPoints(75)\r\nassert(isequal(cans,9), \"right number of cans\");\r\nassert(isequal(balls,19), \"right number of balls\");\r\n%%\r\n[cans, balls] = findPoints(35)\r\nassert(isequal(cans,1), \"right number of cans\");\r\nassert(isequal(balls,11), \"right number of balls\");\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":542228,"edited_by":223089,"edited_at":"2022-10-14T07:06:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":264,"test_suite_updated_at":"2022-09-13T17:30:46.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T14:47:10.000Z","updated_at":"2026-03-30T16:31:13.000Z","published_at":"2022-09-13T14:47:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt was announced during a Robotics Competition kick off that two of the trickiest scoring objects are: soup cans, and beach balls.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe beach ball is worth ten more points than the cans.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe sum of twice the cans points plus three times the beach ball points, is N.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":463,"title":"Looking for Squares","description":"Need n squares that equal one square all together, none zero, none fractured. For example, calling squares(2) should output [16 9] or [25 144] etc, because 16=4*4, 9=3*3, and 16+9=5*5, similarly 25=5*5, 144=12*12, and 25+144=13*13.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373px 8px; transform-origin: 373px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNeed n squares that equal one square all together, none zero, none fractured. For example, calling squares(2) should output [16 9] or [25 144] etc, because 16=4*4, 9=3*3, and 16+9=5*5, similarly 25=5*5, 144=12*12, and 25+144=13*13.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function sq = squares(n)\r\n  sq=[1 4 25 144];\r\nend","test_suite":"%%\r\nfor n=3:7;\r\n   sq=squares(n);\r\n   assert(length(sq)==n)\r\n   for k=1:n\r\n      assert(sq(k)\u003e0)\r\n      assert(round(sqrt(sq(k)))==sqrt(sq(k)))\r\n   end\r\n   assert(round(sqrt(sum(sq)))==sqrt(sum(sq)))\r\nend\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":166,"edited_by":223089,"edited_at":"2023-02-21T05:30:33.000Z","deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2023-02-21T05:30:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-07T08:17:03.000Z","updated_at":"2025-05-16T15:38:29.000Z","published_at":"2012-03-07T08:25:05.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeed n squares that equal one square all together, none zero, none fractured. For example, calling squares(2) should output [16 9] or [25 144] etc, because 16=4*4, 9=3*3, and 16+9=5*5, similarly 25=5*5, 144=12*12, and 25+144=13*13.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60978,"title":"Mesh the octahedron","description":"Problem statement\r\n\r\nAn octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five well known platonic solids.\r\nA triangulated mesh -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this octahedron. To do so, you will list the triangles/rows in a matrix of triangles, T. You will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles [1, 2, 3] and [3, 2, 1] are distinct).\r\nOn the other hand [1, 2, 3], [2, 3, 1] and [3, 1, 2] are one same unique triangle.\r\nThe row order of the triangles in the list doesn't matter.\r\n\r\nEdit / update\r\nTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\r\n\r\nExample\r\nThe first triangle (X \u003e 0, Y \u003e 0, and Z \u003e 0) here can be [1, 2, 5] if counterclockwise oriented (normals are outward oriented).\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1200.23px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 600.117px; transform-origin: 408px 600.117px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373.817px 8px; transform-origin: 373.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five well known platonic solids.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.542px 8px; transform-origin: 157.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.533px 8px; transform-origin: 206.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 327.242px 8px; transform-origin: 327.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this octahedron. To do so, you will list the triangles/rows in a matrix of triangles, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.51667px 8px; transform-origin: 7.51667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.9333px 8px; transform-origin: 49.9333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 2, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.0583px 8px; transform-origin: 40.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are distinct).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the other hand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[2, 3, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 1, 2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5333px 8px; transform-origin: 94.5333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are one same unique triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.9833px 8px; transform-origin: 41.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdit / update\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 351.75px 8px; transform-origin: 351.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.1167px 8px; transform-origin: 52.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.2583px 8px; transform-origin: 75.2583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(X \u0026gt; 0, Y \u0026gt; 0, and Z \u0026gt; 0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 5]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 187.5px 8px; transform-origin: 187.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented (normals are outward oriented).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_octahedron()\r\n  T = 1;\r\nend","test_suite":"%%\r\nT_correct = [1 2 5;\r\n             2 3 5;\r\n             3 4 5;\r\n             4 1 5;\r\n             2 1 6;\r\n             3 2 6;\r\n             4 3 6;\r\n             1 4 6];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_octahedron(),2)),sortrows(sort(T_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_octahedron.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:44:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2025-07-23T16:11:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T08:24:47.000Z","updated_at":"2026-03-31T18:40:36.000Z","published_at":"2025-07-23T09:23:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five well known platonic solids.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh this octahedron. To do so, you will list the triangles/rows in a matrix of triangles, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are distinct).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[2, 3, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are one same unique triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEdit / update\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(X \u0026gt; 0, Y \u0026gt; 0, and Z \u0026gt; 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented (normals are outward oriented).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"378\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"504\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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all the three given point in the same line?","description":"In this problem the input is the coordinate of the three points in a XY plane?\r\n\r\nP1(X1,Y1)\r\n\r\nP2(X2,Y2)\r\n\r\nP3(X3,Y3)\r\n\r\nhow can we find out if all the three points are on the same line or not?\r\n\r\nfor example the points (1,1) , (-1,-1) , (0,0) are on the line y=x.","description_html":"\u003cp\u003eIn this problem the input is the coordinate of the three points in a XY plane?\u003c/p\u003e\u003cp\u003eP1(X1,Y1)\u003c/p\u003e\u003cp\u003eP2(X2,Y2)\u003c/p\u003e\u003cp\u003eP3(X3,Y3)\u003c/p\u003e\u003cp\u003ehow can we find out if all the three points are on the same line or not?\u003c/p\u003e\u003cp\u003efor example the points (1,1) , (-1,-1) , (0,0) are on the line y=x.\u003c/p\u003e","function_template":"% inputs are vectors;\r\n% X=[x1 x2 x3];\r\n% Y=[y1 y2 y3];\r\nfunction y = your_fcn_name(X,Y)\r\n  y = true;\r\nend","test_suite":"%%\r\nX = [-1 1 0];\r\nY=[-1 1 0];\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(X,Y),y_correct))\r\n\r\n%%\r\nX = [0 3 6];\r\nY=[5 7 9];\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(X,Y),y_correct))\r\n\r\n%%\r\nX = [0 7 14];\r\nY=[-7 -5 -3];\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(X,Y),y_correct))\r\n\r\n%%\r\nX = [10 12 -10];\r\nY=[-7 -3 47];\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(X,Y),y_correct))\r\n\r\n%%\r\nX = [0 0.8 1];\r\nY=[0.2 1 1];\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(X,Y),y_correct))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":1,"created_by":4320,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":603,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":17,"created_at":"2012-06-15T13:30:42.000Z","updated_at":"2026-03-13T04:50:21.000Z","published_at":"2012-06-15T13:30:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem the input is the coordinate of the three points in a XY plane?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP1(X1,Y1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP2(X2,Y2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP3(X3,Y3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehow can we find out if all the three points are on the same line or not?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efor example the points (1,1) , (-1,-1) , (0,0) are on the line y=x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":57447,"title":"Compute a nested cube root","description":"Consider the quantity . Write a function to compute  without using loops or recursion. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.075px 8px; transform-origin: 68.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the quantity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\" style=\"width: 249px; height: 19.5px;\" width=\"249\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.875px 8px; transform-origin: 90.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Write a function to compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71.575px 8px; transform-origin: 71.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e without using loops or recursion. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = nestedCubeRoot(a)\r\n  y = nthroot(a+nthroot(a+nthroot(a+nthroot(a,3),3),3),3);\r\nend","test_suite":"%%\r\na = 6;\r\nassert(abs(nestedCubeRoot(a)-2)\u003c1e-14)\r\n\r\n%%\r\na = 24;\r\nassert(abs(nestedCubeRoot(a)-3)\u003c1e-14)\r\n\r\n%%\r\na = 120;\r\nassert(abs(nestedCubeRoot(a)-5)\u003c1e-14)\r\n\r\n%%\r\na = 336;\r\nassert(abs(nestedCubeRoot(a)-7)\u003c1e-14)\r\n\r\n%%\r\na = 1320;\r\nassert(abs(nestedCubeRoot(a)-11)\u003c1e-14)\r\n\r\n%%\r\na = 15/8;\r\nassert(abs(nestedCubeRoot(a)-3/2)\u003c1e-14)\r\n\r\n%%\r\na = 2040/2197;\r\nassert(abs(nestedCubeRoot(a)-17/13)\u003c1e-14)\r\n\r\n%%\r\na = 9048/12167;\r\nassert(abs(nestedCubeRoot(a)-29/23)\u003c1e-14)\r\n\r\n%%\r\na = 29520/29791;\r\nassert(abs(nestedCubeRoot(a)-41/31)\u003c1e-14)\r\n\r\n%%\r\na = 117384/226981;\r\nassert(abs(nestedCubeRoot(a)-73/61)\u003c1e-14)\r\n\r\n%%\r\na = 2259912/3869893;\r\nassert(abs(nestedCubeRoot(a)-191/157)\u003c1e-14)\r\n\r\n%%\r\nfiletext = fileread('nestedCubeRoot.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'switch') || contains(filetext,'for') || contains(filetext,'while') || length(strfind(filetext,'nestedCubeRoot')) \u003e 1;\r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-21T13:18:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-21T13:13:13.000Z","updated_at":"2026-03-04T12:08:30.000Z","published_at":"2022-12-21T13:18:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the quantity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = (a+(a+(a+(a+\\\\ldots)^{1/3})^{1/3})^{1/3})^{1/3}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Write a function to compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e without using loops or recursion. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42384,"title":"Combined Ages 2 - Symmetric, n ≥ 3","description":"Following on \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42382-combined-ages-1-symmetric-n-3 Combined Ages 2\u003e, you will now be provided with age sums for _n_ individuals where _n_ ≥ 3. The sums will be provided in sorted order and will be for _n–1_ individuals (e.g., A+B+C, A+B+D, A+C+D, B+C+D). See the previous problem for an explanation, the test suite for examples, and the problem tags for hints.","description_html":"\u003cp\u003eFollowing on \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42382-combined-ages-1-symmetric-n-3\"\u003eCombined Ages 2\u003c/a\u003e, you will now be provided with age sums for \u003ci\u003en\u003c/i\u003e individuals where \u003ci\u003en\u003c/i\u003e ≥ 3. The sums will be provided in sorted order and will be for \u003ci\u003en–1\u003c/i\u003e individuals (e.g., A+B+C, A+B+D, A+C+D, B+C+D). See the previous problem for an explanation, the test suite for examples, and the problem tags for hints.\u003c/p\u003e","function_template":"function y = combined_ages2(varargin)\r\n y = ones(nargin,1);\r\nend","test_suite":"%%\r\nAB = 43;\r\nAC = 66;\r\nBC = 55;\r\ny = combined_ages2(AB,AC,BC);\r\ny_correct = [27 16 39];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 30;\r\nAC = 40;\r\nBC = 50;\r\ny = combined_ages2(AB,AC,BC);\r\ny_correct = [10 20 30];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABC = 72;\r\nABD = 66;\r\nACD = 70;\r\nBCD = 77;\r\ny = combined_ages2(ABC,ABD,ACD,BCD);\r\ny_correct = [18 25 29 23];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABC = 66;\r\nABD = 67;\r\nACD = 68;\r\nBCD = 69;\r\ny = combined_ages2(ABC,ABD,ACD,BCD);\r\ny_correct = [21 22 23 24];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABC = 60;\r\nABD = 65;\r\nACD = 70;\r\nBCD = 75;\r\ny = combined_ages2(ABC,ABD,ACD,BCD);\r\ny_correct = [15 20 25 30];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCD = 90;\r\nABCE = 115;\r\nABDE = 100;\r\nACDE = 110;\r\nBCDE = 105;\r\ny = combined_ages2(ABCD,ABCE,ABDE,ACDE,BCDE);\r\ny_correct = [25 20 30 15 40];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCD = 44;\r\nABCE = 37;\r\nABDE = 47;\r\nACDE = 51;\r\nBCDE = 53;\r\ny = combined_ages2(ABCD,ABCE,ABDE,ACDE,BCDE);\r\ny_correct = [5 7 11 21 14];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCDEF = 133;\r\nABCDEG = 186;\r\nABCDFG = 172;\r\nABCEFG = 163;\r\nABDEFG = 192;\r\nACDEFG = 200;\r\nBCDEFG = 184;\r\ny = combined_ages2(ABCDEF,ABCDEG,ABCDFG,ABCEFG,ABDEFG,ACDEFG,BCDEFG);\r\ny_correct = [21 5 13 42 33 19 72];\r\nfor i = 1:numel(y_correct)\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":183,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-16T19:13:14.000Z","updated_at":"2026-03-29T21:29:20.000Z","published_at":"2015-06-16T19:13:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollowing on\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42382-combined-ages-1-symmetric-n-3\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCombined Ages 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, you will now be provided with age sums for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e individuals where\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 3. The sums will be provided in sorted order and will be for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en–1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e individuals (e.g., A+B+C, A+B+D, A+C+D, B+C+D). See the previous problem for an explanation, the test suite for examples, and the problem tags for hints.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42385,"title":"Combined Ages 4 - Non-symmetric with multiples, n ≥ 3","description":"This problem is slightly more difficult than \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42383-combined-ages-3-non-symmetric-n-3 Combined Ages 3\u003e. In this case, some of the sums may include multiples of some individuals' ages. As an example: If the ages of all three individuals with Chris's age added again sum to 98, the ages of Barry (twice) and Chris sum to 84, and the ages of Alex (twice) and Barry sum to 70, what are their individual ages?\r\n\r\nThe individuals will be represented by the first n capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:\r\n\r\n* A+B+C+C = ABCC (= 98)\r\n* B+B+C = BBC (= 84)\r\n* A+A+B = AAB (= 70)\r\n\r\nThough the variables are ordered above, they will not always be in the test cases. Write a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.","description_html":"\u003cp\u003eThis problem is slightly more difficult than \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42383-combined-ages-3-non-symmetric-n-3\"\u003eCombined Ages 3\u003c/a\u003e. In this case, some of the sums may include multiples of some individuals' ages. As an example: If the ages of all three individuals with Chris's age added again sum to 98, the ages of Barry (twice) and Chris sum to 84, and the ages of Alex (twice) and Barry sum to 70, what are their individual ages?\u003c/p\u003e\u003cp\u003eThe individuals will be represented by the first n capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:\u003c/p\u003e\u003cul\u003e\u003cli\u003eA+B+C+C = ABCC (= 98)\u003c/li\u003e\u003cli\u003eB+B+C = BBC (= 84)\u003c/li\u003e\u003cli\u003eA+A+B = AAB (= 70)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThough the variables are ordered above, they will not always be in the test cases. Write a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.\u003c/p\u003e","function_template":"function y = combined_ages_nonsymmetric_w_mult(varargin)\r\n y = ones(nargin,1);\r\nend","test_suite":"%%\r\nABCD = 70;\r\nABC = 65;\r\nAB = 40;\r\nBC = 52;\r\ny = combined_ages_nonsymmetric_w_mult(ABCD,ABC,AB,BC);\r\ny_correct = [13;27;25;5];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCC = 98;\r\nBBC = 84;\r\nAAB = 70;\r\ny = combined_ages_nonsymmetric_w_mult(ABCC,BBC,AAB);\r\ny_correct = [20;30;24];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCDA = 150;\r\nABCB = 99;\r\nBCDB = 91;\r\nABDAD = 135;\r\ny = combined_ages_nonsymmetric_w_mult(ABCDA,ABCB,BCDB,ABDAD);\r\ny_correct = [35;11;42;27];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABBA = 90;\r\nBCC = 113;\r\nABCBA = 141;\r\ny = combined_ages_nonsymmetric_w_mult(ABBA,BCC,ABCBA);\r\ny_correct = [34;11;51];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCDE = 120;\r\nABCDD = 111;\r\nABCCC = 87;\r\nABBBB = 66;\r\nAAAAA = 50;\r\ny = combined_ages_nonsymmetric_w_mult(ABCDE,ABCDD,ABCCC,ABBBB,AAAAA);\r\ny_correct = [10,14,21,33,42];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABC = 45;\r\nBEA = 66;\r\nCAE = 73;\r\nDAB = 57;\r\nAAD = 53;\r\ny = combined_ages_nonsymmetric_w_mult(ABC,BEA,CAE,DAB,AAD);\r\ny_correct = [10,14,21,33,42];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCABC = 144;\r\nBEAB = 107;\r\nCAEAD = 147;\r\nDABB = 73;\r\nAADAA = 133;\r\ny = combined_ages_nonsymmetric_w_mult(ABCABC,BEAB,CAEAD,DABB,AADAA);\r\ny_correct = [30,15,27,13,47];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%% anti-cheating test case\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tABCC = 98;\r\n\t\tBBC = 84;\r\n\t\tAAB = 70;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCC,BBC,AAB);\r\n\t\ty_correct = [20;30;24];\r\n\tcase 2\r\n\t\tABCDA = 150;\r\n\t\tABCB = 99;\r\n\t\tBCDB = 91;\r\n\t\tABDAD = 135;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCDA,ABCB,BCDB,ABDAD);\r\n\t\ty_correct = [35;11;42;27];\r\n\tcase 3\r\n\t\tABCABC = 144;\r\n\t\tBEAB = 107;\r\n\t\tCAEAD = 147;\r\n\t\tDABB = 73;\r\n\t\tAADAA = 133;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCABC,BEAB,CAEAD,DABB,AADAA);\r\n\t\ty_correct = [30,15,27,13,47];\r\n\tcase 4\r\n\t\tABCD = 70;\r\n\t\tABC = 65;\r\n\t\tAB = 40;\r\n\t\tBC = 52;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCD,ABC,AB,BC);\r\n\t\ty_correct = [13;27;25;5];\r\nend\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%% anti-cheating test case\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tABCC = 98;\r\n\t\tBBC = 84;\r\n\t\tAAB = 70;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCC,BBC,AAB);\r\n\t\ty_correct = [20;30;24];\r\n\tcase 2\r\n\t\tABCABC = 144;\r\n\t\tBEAB = 107;\r\n\t\tCAEAD = 147;\r\n\t\tDABB = 73;\r\n\t\tAADAA = 133;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCABC,BEAB,CAEAD,DABB,AADAA);\r\n\t\ty_correct = [30,15,27,13,47];\r\n\tcase 3\r\n\t\tABCD = 70;\r\n\t\tABC = 65;\r\n\t\tAB = 40;\r\n\t\tBC = 52;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCD,ABC,AB,BC);\r\n\t\ty_correct = [13;27;25;5];\r\n\tcase 4\r\n\t\tABC = 45;\r\n\t\tBEA = 66;\r\n\t\tCAE = 73;\r\n\t\tDAB = 57;\r\n\t\tAAD = 53;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABC,BEA,CAE,DAB,AAD);\r\n\t\ty_correct = [10,14,21,33,42];\r\nend\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%% anti-cheating test case\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tABBA = 90;\r\n\t\tBCC = 113;\r\n\t\tABCBA = 141;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABBA,BCC,ABCBA);\r\n\t\ty_correct = [34;11;51];\r\n\tcase 2\r\n\t\tABCD = 70;\r\n\t\tABC = 65;\r\n\t\tAB = 40;\r\n\t\tBC = 52;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCD,ABC,AB,BC);\r\n\t\ty_correct = [13;27;25;5];\r\n\tcase 3\r\n\t\tABCDA = 150;\r\n\t\tABCB = 99;\r\n\t\tBCDB = 91;\r\n\t\tABDAD = 135;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCDA,ABCB,BCDB,ABDAD);\r\n\t\ty_correct = [35;11;42;27];\r\n\tcase 4\r\n\t\tABCC = 98;\r\n\t\tBBC = 84;\r\n\t\tAAB = 70;\r\n\t\ty = combined_ages_nonsymmetric_w_mult(ABCC,BBC,AAB);\r\n\t\ty_correct = [20;30;24];\r\nend\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":122,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-16T20:03:26.000Z","updated_at":"2026-03-24T04:49:54.000Z","published_at":"2015-06-16T20:03:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is slightly more difficult than\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42383-combined-ages-3-non-symmetric-n-3\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCombined Ages 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. In this case, some of the sums may include multiples of some individuals' ages. As an example: If the ages of all three individuals with Chris's age added again sum to 98, the ages of Barry (twice) and Chris sum to 84, and the ages of Alex (twice) and Barry sum to 70, what are their individual ages?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe individuals will be represented by the first n capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+B+C+C = ABCC (= 98)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eB+B+C = BBC (= 84)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+A+B = AAB (= 70)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThough the variables are ordered above, they will not always be in the test cases. Write a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42383,"title":"Combined Ages 3 - Non-symmetric, n ≥ 3","description":"Pursuant to the previous two problems ( \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42382-combined-ages-1-symmetric-n-3 Symmetric, n = 3\u003e and \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42384-combined-ages-2-symmetric-n-3 Symmetric, n ≥ 3\u003e ), this problem will provide _n_ combined ages where _n_ is the number of individuals, though the age sums will not form a symmetric matrix. As an example: If the ages of all four individuals sum to 70; the ages of Alex, Barry, and Chris sum to 65; the ages of Alex and Barry sum to 40; and the ages of Barry and Chris sum to 52, what are their individual ages?\r\n\r\nThe individuals will be represented by the first _n_ capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:\r\n\r\n* A+B+C+D = ABCD (= 70)\r\n* A+B+C = ABC (= 65)\r\n* A+B = AB (= 40)\r\n* B+C = BC (= 52)\r\n\r\nWrite a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.","description_html":"\u003cp\u003ePursuant to the previous two problems ( \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42382-combined-ages-1-symmetric-n-3\"\u003eSymmetric, n = 3\u003c/a\u003e and \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42384-combined-ages-2-symmetric-n-3\"\u003eSymmetric, n ≥ 3\u003c/a\u003e ), this problem will provide \u003ci\u003en\u003c/i\u003e combined ages where \u003ci\u003en\u003c/i\u003e is the number of individuals, though the age sums will not form a symmetric matrix. As an example: If the ages of all four individuals sum to 70; the ages of Alex, Barry, and Chris sum to 65; the ages of Alex and Barry sum to 40; and the ages of Barry and Chris sum to 52, what are their individual ages?\u003c/p\u003e\u003cp\u003eThe individuals will be represented by the first \u003ci\u003en\u003c/i\u003e capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:\u003c/p\u003e\u003cul\u003e\u003cli\u003eA+B+C+D = ABCD (= 70)\u003c/li\u003e\u003cli\u003eA+B+C = ABC (= 65)\u003c/li\u003e\u003cli\u003eA+B = AB (= 40)\u003c/li\u003e\u003cli\u003eB+C = BC (= 52)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eWrite a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.\u003c/p\u003e","function_template":"function y = combined_ages_nonsymmetric(varargin)\r\n y = ones(nargin,1);\r\nend","test_suite":"%%\r\nABCD = 70;\r\nABC = 65;\r\nAB = 40;\r\nBC = 52;\r\ny = combined_ages_nonsymmetric(ABCD,ABC,AB,BC);\r\ny_correct = [13;27;25;5];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABC = 70;\r\nBC = 50;\r\nAC = 40;\r\ny = combined_ages_nonsymmetric(ABC,BC,AC);\r\ny_correct = [20;30;20];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCD = 100;\r\nABC = 80;\r\nBCD = 70;\r\nABD = 60;\r\ny = combined_ages_nonsymmetric(ABCD,ABC,BCD,ABD);\r\ny_correct = [30;10;40;20];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 34;\r\nBC = 54;\r\nABC = 86;\r\ny = combined_ages_nonsymmetric(AB,BC,ABC);\r\ny_correct = [32;2;52];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nABCDE = 120;\r\nABCD = 78;\r\nABC = 45;\r\nAB = 24;\r\nAC = 31;\r\ny = combined_ages_nonsymmetric(ABCDE,ABCD,ABC,AB,AC);\r\ny_correct = [10,14,21,33,42];\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [37 33 31 38];\r\nABC = y_correct(1) + y_correct(2) + y_correct(3);\r\nBCD = y_correct(2) + y_correct(3) + y_correct(4);\r\nACD = y_correct(1) + y_correct(3) + y_correct(4);\r\nABD = y_correct(1) + y_correct(2) + y_correct(4);\r\ny = combined_ages_nonsymmetric(ABC,BCD,ACD,ABD);\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [5 15 30 62 100];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\nACE = y_correct(1) + y_correct(3) + y_correct(5);\r\nABDE = y_correct(1) + y_correct(2) + y_correct(4) + y_correct(5);\r\ny = combined_ages_nonsymmetric(AB,BC,AC,ACE,ABDE);\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [2 3 5 7 11 17 23 31 42 55];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\nABCD = y_correct(1) + y_correct(2) + y_correct(3) + y_correct(4);\r\nCDEG = y_correct(3) + y_correct(4) + y_correct(5) + y_correct(7);\r\nBFH = y_correct(2) + y_correct(6) + y_correct(8);\r\nFGIJ = y_correct(6) + y_correct(7) + y_correct(9) + y_correct(10);\r\nACEGH = y_correct(1) + y_correct(3) + y_correct(5) + y_correct(7) + y_correct(8);\r\nBEJ = y_correct(2) + y_correct(5) + y_correct(10);\r\nABDIJ = y_correct(1) + y_correct(2) + y_correct(4) + y_correct(9) + y_correct(10);\r\ny = combined_ages_nonsymmetric(AB,BC,AC,ABCD,CDEG,BFH,FGIJ,ACEGH,BEJ,ABDIJ);\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%% anti-cheating test case\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tABCD = 70;\r\n\t\tABC = 65;\r\n\t\tAB = 40;\r\n\t\tBC = 52;\r\n\t\ty = combined_ages_nonsymmetric(ABCD,ABC,AB,BC);\r\n\t\ty_correct = [13;27;25;5];\r\n\tcase 2\r\n\t\tABCD = 100;\r\n\t\tABC = 80;\r\n\t\tBCD = 70;\r\n\t\tABD = 60;\r\n\t\ty = combined_ages_nonsymmetric(ABCD,ABC,BCD,ABD);\r\n\t\ty_correct = [30;10;40;20];\r\n\tcase 3\r\n\t\tAB = 34;\r\n\t\tBC = 54;\r\n\t\tABC = 86;\r\n\t\ty = combined_ages_nonsymmetric(AB,BC,ABC);\r\n\t\ty_correct = [32;2;52];\r\n\tcase 4\r\n\t\tABC = 70;\r\n\t\tBC = 50;\r\n\t\tAC = 40;\r\n\t\ty = combined_ages_nonsymmetric(ABC,BC,AC);\r\n\t\ty_correct = [20;30;20];\r\nend\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%% anti-cheating test case\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tABC = 70;\r\n\t\tBC = 50;\r\n\t\tAC = 40;\r\n\t\ty = combined_ages_nonsymmetric(ABC,BC,AC);\r\n\t\ty_correct = [20;30;20];\r\n\tcase 2\r\n\t\tAB = 34;\r\n\t\tBC = 54;\r\n\t\tABC = 86;\r\n\t\ty = combined_ages_nonsymmetric(AB,BC,ABC);\r\n\t\ty_correct = [32;2;52];\r\n\tcase 3\r\n\t\tABCD = 70;\r\n\t\tABC = 65;\r\n\t\tAB = 40;\r\n\t\tBC = 52;\r\n\t\ty = combined_ages_nonsymmetric(ABCD,ABC,AB,BC);\r\n\t\ty_correct = [13;27;25;5];\r\n\tcase 4\r\n\t\tABCD = 100;\r\n\t\tABC = 80;\r\n\t\tBCD = 70;\r\n\t\tABD = 60;\r\n\t\ty = combined_ages_nonsymmetric(ABCD,ABC,BCD,ABD);\r\n\t\ty_correct = [30;10;40;20];\r\nend\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%% anti-cheating test case\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tAB = 34;\r\n\t\tBC = 54;\r\n\t\tABC = 86;\r\n\t\ty = combined_ages_nonsymmetric(AB,BC,ABC);\r\n\t\ty_correct = [32;2;52];\r\n\tcase 2\r\n\t\tABCD = 100;\r\n\t\tABC = 80;\r\n\t\tBCD = 70;\r\n\t\tABD = 60;\r\n\t\ty = combined_ages_nonsymmetric(ABCD,ABC,BCD,ABD);\r\n\t\ty_correct = [30;10;40;20];\r\n\tcase 3\r\n\t\tABCD = 70;\r\n\t\tABC = 65;\r\n\t\tAB = 40;\r\n\t\tBC = 52;\r\n\t\ty = combined_ages_nonsymmetric(ABCD,ABC,AB,BC);\r\n\t\ty_correct = [13;27;25;5];\r\n\tcase 4\r\n\t\tABC = 70;\r\n\t\tBC = 50;\r\n\t\tAC = 40;\r\n\t\ty = combined_ages_nonsymmetric(ABC,BC,AC);\r\n\t\ty_correct = [20;30;20];\r\nend\r\nfor i = 1:numel(y_correct)\r\n\tassert(isequal(y(i),y_correct(i)))\r\nend\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":144,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-16T18:34:18.000Z","updated_at":"2026-03-29T22:25:18.000Z","published_at":"2015-06-16T18:34:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePursuant to the previous two problems (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42382-combined-ages-1-symmetric-n-3\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSymmetric, n = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42384-combined-ages-2-symmetric-n-3\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSymmetric, n ≥ 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ), this problem will provide\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e combined ages where\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of individuals, though the age sums will not form a symmetric matrix. As an example: If the ages of all four individuals sum to 70; the ages of Alex, Barry, and Chris sum to 65; the ages of Alex and Barry sum to 40; and the ages of Barry and Chris sum to 52, what are their individual ages?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe individuals will be represented by the first\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+B+C+D = ABCD (= 70)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+B+C = ABC (= 65)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+B = AB (= 40)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eB+C = BC (= 52)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52861,"title":"Easy Sequences 37: Natural Factorable Polynomials","description":"A polynomial of the form: , for , is said to be natural factorable if it can be factored into products of first degree binomials: , where,  and  are all natural numbers (i.e. integers that are ).\r\nGiven an integer , write a function that counts the number of all possible natural factorable polynomials that can be formed, wherein .\r\nFor example, when , the are  possible natural factorable polynomials, namely:\r\n                                    ;\r\n                                    ;\r\n                                    ;\r\n                                    ;\r\n                                    \r\n                                    ; and\r\n                                    \r\nTherefore the function output should be .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 384px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA polynomial of the form: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"287.5\" height=\"21\" style=\"width: 287.5px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, is said to be natural factorable if it can be factored into products of first degree binomials: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"214.5\" height=\"20\" style=\"width: 214.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, where, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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width=\"140\" height=\"20\" style=\"width: 140px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"131.5\" height=\"20\" style=\"width: 131.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eall\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e natural numbers (i.e. integers that are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"25\" height=\"18\" style=\"width: 25px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, write a function that counts the number of all possible natural factorable polynomials that can be formed, wherein \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"67.5\" height=\"20\" style=\"width: 67.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, when \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, the are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e7\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e possible natural factorable polynomials, namely:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"212.5\" height=\"20\" style=\"width: 212.5px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore the function output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e7\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = numPols(a)\r\n  y = x;\r\nend","test_suite":"%%\r\na = 4;\r\nn_correct = 7;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\na = 5;\r\nn_correct = 13;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\na = 10;\r\nn_correct = 128;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\na = 20;\r\nn_correct = 2693;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\na = 50;\r\nn_correct = 1295920;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\nas = 51:150;\r\nns = arrayfun(@(a) numPols(a),as);\r\nss = int64([sum(ns) ns(1:20:end) floor(std(ns))])\r\nss_correct = [4267039260053 1535862 34751087 529784816 6145056743 58130508732 88934830907];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\na = 75;\r\nn_correct = 61537319;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\na = 100;\r\nn_correct = 1642992467;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\na = 150;\r\nn_correct = 423652454768;\r\nassert(isequal(numPols(a),n_correct))\r\n%%\r\nfiletext = fileread('numPols.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-06T10:42:04.000Z","updated_at":"2026-02-24T17:43:19.000Z","published_at":"2021-10-07T11:06:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA polynomial of the form: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^n+a_2x^{n-1}+a_3x^{n-2}+...+a_{n-2}x^2+a_{n-1}x+a_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026gt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is said to be natural factorable if it can be factored into products of first degree binomials: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x+r_1)(x+r_2)...(x+r_{n-1})(x+r_n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_2,\\\\ a_3,\\\\ a_4,\\\\ ...\\\\ a_{n-1},\\\\ a_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_1,\\\\ r_2,\\\\ r_3,\\\\ ...\\\\ r_{n-1},\\\\ r_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eall\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e natural numbers (i.e. integers that are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ge1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a function that counts the number of all possible natural factorable polynomials that can be formed, wherein \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \u0026lt; a_2\\\\le a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, when \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e possible natural factorable polynomials, namely:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^2+2x+1=(x+1)^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^2+3x+2=(x+1)(x+2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^2+4x+3 = (x+1)(x+3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^2+4x+4 = (x+2)^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^3+3x^2+3x+1=(x+1)^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^3+4x^2+5x+2 = (x+1)^2(x+2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^4+4x^3+6x^2+4x+1=(x+1)^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore the function output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"algebra\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"algebra\"","current_player":null,"sort":"map(difficulty_value,0,0,999) 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