{"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":1283,"title":"Points on a Sphere","description":"Given a sphere of radius R, determine how many points on the surface of that sphere have three integer coordinates.  Do not output the actual coordinates, but just the number of points.\r\n\r\nFor example, a sphere of radius 1 has 6 points with three integer coordinates:\r\n\r\n* (1,0,0)\r\n* (-1,0,0)\r\n* (0,-1,0)\r\n* (0,1,0)\r\n* (0,0,1)\r\n* (0,0,-1)\r\n\r\nYour output of surface_points(1) would be 6.  Good luck!","description_html":"\u003cp\u003eGiven a sphere of radius R, determine how many points on the surface of that sphere have three integer coordinates.  Do not output the actual coordinates, but just the number of points.\u003c/p\u003e\u003cp\u003eFor example, a sphere of radius 1 has 6 points with three integer coordinates:\u003c/p\u003e\u003cul\u003e\u003cli\u003e(1,0,0)\u003c/li\u003e\u003cli\u003e(-1,0,0)\u003c/li\u003e\u003cli\u003e(0,-1,0)\u003c/li\u003e\u003cli\u003e(0,1,0)\u003c/li\u003e\u003cli\u003e(0,0,1)\u003c/li\u003e\u003cli\u003e(0,0,-1)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eYour output of surface_points(1) would be 6.  Good luck!\u003c/p\u003e","function_template":"function y = surface_points(r)\r\ny=6;\r\nend","test_suite":"%%\r\nx = 1; y_correct = 6;\r\nassert(isequal(surface_points(x),y_correct))\r\n%%\r\nx = 1024; y_correct = 6;\r\nassert(isequal(surface_points(x),y_correct))\r\n%%\r\nx = 7581; y_correct = 108270;\r\nassert(isequal(surface_points(x),y_correct))\r\n%%\r\nx = 450; y_correct = 2550;\r\nassert(isequal(surface_points(x),y_correct))\r\n%%\r\nx = 123456; y_correct = 19350;\r\nassert(isequal(surface_points(x),y_correct))\r\n%%\r\nx=ceil(rand*8); y_correct=[6 30 30 150 510 4590 4590 43470];\r\nassert(isequal(surface_points(factorial(x+1)),y_correct(x)))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2013-02-22T17:25:38.000Z","rescore_all_solutions":false,"group_id":20,"created_at":"2013-02-20T16:48:12.000Z","updated_at":"2026-02-16T11:16:05.000Z","published_at":"2013-02-20T16:49:36.000Z","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 sphere of radius R, determine how many points on the surface of that sphere have three integer coordinates. Do not output the actual coordinates, but just the number of points.\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, a sphere of radius 1 has 6 points with three integer coordinates:\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\u003e(1,0,0)\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\u003e(-1,0,0)\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\u003e(0,-1,0)\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\u003e(0,1,0)\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\u003e(0,0,1)\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\u003e(0,0,-1)\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\u003eYour output of surface_points(1) would be 6. Good luck!\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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":1283,"title":"Points on a Sphere","description":"Given a sphere of radius R, determine how many points on the surface of that sphere have three integer coordinates.  Do not output the actual coordinates, but just the number of points.\r\n\r\nFor example, a sphere of radius 1 has 6 points with three integer coordinates:\r\n\r\n* (1,0,0)\r\n* (-1,0,0)\r\n* (0,-1,0)\r\n* (0,1,0)\r\n* (0,0,1)\r\n* (0,0,-1)\r\n\r\nYour output of surface_points(1) would be 6.  Good luck!","description_html":"\u003cp\u003eGiven a sphere of radius R, determine how many points on the surface of that sphere have three integer coordinates.  Do not output the actual coordinates, but just the number of points.\u003c/p\u003e\u003cp\u003eFor example, a sphere of radius 1 has 6 points with three integer coordinates:\u003c/p\u003e\u003cul\u003e\u003cli\u003e(1,0,0)\u003c/li\u003e\u003cli\u003e(-1,0,0)\u003c/li\u003e\u003cli\u003e(0,-1,0)\u003c/li\u003e\u003cli\u003e(0,1,0)\u003c/li\u003e\u003cli\u003e(0,0,1)\u003c/li\u003e\u003cli\u003e(0,0,-1)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eYour output of surface_points(1) would be 6.  Good luck!\u003c/p\u003e","function_template":"function y = surface_points(r)\r\ny=6;\r\nend","test_suite":"%%\r\nx = 1; y_correct = 6;\r\nassert(isequal(surface_points(x),y_correct))\r\n%%\r\nx = 1024; y_correct = 6;\r\nassert(isequal(surface_points(x),y_correct))\r\n%%\r\nx = 7581; y_correct = 108270;\r\nassert(isequal(surface_points(x),y_correct))\r\n%%\r\nx = 450; y_correct = 2550;\r\nassert(isequal(surface_points(x),y_correct))\r\n%%\r\nx = 123456; y_correct = 19350;\r\nassert(isequal(surface_points(x),y_correct))\r\n%%\r\nx=ceil(rand*8); y_correct=[6 30 30 150 510 4590 4590 43470];\r\nassert(isequal(surface_points(factorial(x+1)),y_correct(x)))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2013-02-22T17:25:38.000Z","rescore_all_solutions":false,"group_id":20,"created_at":"2013-02-20T16:48:12.000Z","updated_at":"2026-02-16T11:16:05.000Z","published_at":"2013-02-20T16:49:36.000Z","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 sphere of radius R, determine how many points on the surface of that sphere have three integer coordinates. Do not output the actual coordinates, but just the number of points.\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, a sphere of radius 1 has 6 points with three integer coordinates:\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\u003e(1,0,0)\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\u003e(-1,0,0)\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\u003e(0,-1,0)\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\u003e(0,1,0)\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\u003e(0,0,1)\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\u003e(0,0,-1)\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\u003eYour output of surface_points(1) would be 6. Good luck!\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\"}]}"}],"term":"tag:\"surface 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