{"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":44719,"title":"Penny Distribution Machine","description":"A machine consists of a row of boxes. To start, one places N pennies in the leftmost box. The machine then redistributes the pennies as follows:\r\n\r\nOn each iteration, it replaces a pair of pennies in one box with a single penny in the next box to the right. The iterations stop when there is no box with more than one coin. For example, the figure below shows the working of the machine in distributing nine pennies by always selecting a pair of pennies in the leftmost box with at least two coins.\r\n\r\n  Itr 0:   9  0  0  0        \r\n  Itr 1:   7  1  0  0 \r\n  Itr 2:   5  2  0  0  \r\n  Itr 3:   3  3  0  0  \r\n  Itr 4:   1  4  0  0   \r\n  Itr 5:   1  2  1  0   \r\n  Itr 6:   1  0  2  0   \r\n  Itr 7:   1  0  0  1  \r\n\r\nDetermine the number of boxes and iterations needed by the machine to distribute N pennies. From the example above, the machine requires four boxes and seven iterations to distribute nine pennies.\r\n  ","description_html":"\u003cp\u003eA machine consists of a row of boxes. To start, one places N pennies in the leftmost box. The machine then redistributes the pennies as follows:\u003c/p\u003e\u003cp\u003eOn each iteration, it replaces a pair of pennies in one box with a single penny in the next box to the right. The iterations stop when there is no box with more than one coin. For example, the figure below shows the working of the machine in distributing nine pennies by always selecting a pair of pennies in the leftmost box with at least two coins.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eItr 0:   9  0  0  0        \r\nItr 1:   7  1  0  0 \r\nItr 2:   5  2  0  0  \r\nItr 3:   3  3  0  0  \r\nItr 4:   1  4  0  0   \r\nItr 5:   1  2  1  0   \r\nItr 6:   1  0  2  0   \r\nItr 7:   1  0  0  1  \r\n\u003c/pre\u003e\u003cp\u003eDetermine the number of boxes and iterations needed by the machine to distribute N pennies. From the example above, the machine requires four boxes and seven iterations to distribute nine pennies.\u003c/p\u003e","function_template":"function [box, itr] = PDMachine(N)\r\n \r\nend","test_suite":"%%\r\nN = 1;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,1) \u0026 isequal(itr,0))\r\n\r\n%%\r\nN = 2;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,2) \u0026 isequal(itr,1))\r\n\r\n%%\r\nN = 3;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,2) \u0026 isequal(itr,1))\r\n\r\n%%\r\nN = 5;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,3) \u0026 isequal(itr,3))\r\n\r\n%%\r\nN = 10;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,4) \u0026 isequal(itr,8))\r\n\r\n%%\r\nN = 19;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,5) \u0026 isequal(itr,16))\r\n\r\n%%\r\nN = 25;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,5) \u0026 isequal(itr,22))\r\n\r\n%%\r\nN = 50;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,6) \u0026 isequal(itr,47))\r\n\r\n%%\r\nN = 100;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,7) \u0026 isequal(itr,97))\r\n\r\n%%\r\nN = 777;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,10) \u0026 isequal(itr,773))\r\n\r\n%%\r\nN = 1234;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,11) \u0026 isequal(itr,1229))\r\n\r\n%%\r\nN = 5000;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,13) \u0026 isequal(itr,4995))\r\n\r\n%%\r\nN = 9999;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,14) \u0026 isequal(itr,9991))\r\n\r\n%%\r\nN = 100000;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,17) \u0026 isequal(itr,99994))\r\n\r\n%%\r\nN = 1234567;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,21) \u0026 isequal(itr,1234556))\r\n\r\n%%\r\nN = 12345678;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,24) \u0026 isequal(itr,12345666))\r\n\r\n%%\r\nN = 987654321;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,30) \u0026 isequal(itr,987654304))\r\n\r\n%%\r\nN = 1234567890;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,31) \u0026 isequal(itr,1234567878))\r\n\r\n%%\r\nN = 9876543210;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,34) \u0026 isequal(itr,9876543195))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":178544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":"2018-09-18T17:45:21.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-08-05T02:30:50.000Z","updated_at":"2025-12-05T12:14:33.000Z","published_at":"2018-08-05T03:02:52.000Z","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\u003eA machine consists of a row of boxes. To start, one places N pennies in the leftmost box. The machine then redistributes the pennies as follows:\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\u003eOn each iteration, it replaces a pair of pennies in one box with a single penny in the next box to the right. The iterations stop when there is no box with more than one coin. For example, the figure below shows the working of the machine in distributing nine pennies by always selecting a pair of pennies in the leftmost box with at least two coins.\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[Itr 0:   9  0  0  0        \\nItr 1:   7  1  0  0 \\nItr 2:   5  2  0  0  \\nItr 3:   3  3  0  0  \\nItr 4:   1  4  0  0   \\nItr 5:   1  2  1  0   \\nItr 6:   1  0  2  0   \\nItr 7:   1  0  0  1]]\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\u003eDetermine the number of boxes and iterations needed by the machine to distribute N pennies. From the example above, the machine requires four boxes and seven iterations to distribute nine pennies.\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":44719,"title":"Penny Distribution Machine","description":"A machine consists of a row of boxes. To start, one places N pennies in the leftmost box. The machine then redistributes the pennies as follows:\r\n\r\nOn each iteration, it replaces a pair of pennies in one box with a single penny in the next box to the right. The iterations stop when there is no box with more than one coin. For example, the figure below shows the working of the machine in distributing nine pennies by always selecting a pair of pennies in the leftmost box with at least two coins.\r\n\r\n  Itr 0:   9  0  0  0        \r\n  Itr 1:   7  1  0  0 \r\n  Itr 2:   5  2  0  0  \r\n  Itr 3:   3  3  0  0  \r\n  Itr 4:   1  4  0  0   \r\n  Itr 5:   1  2  1  0   \r\n  Itr 6:   1  0  2  0   \r\n  Itr 7:   1  0  0  1  \r\n\r\nDetermine the number of boxes and iterations needed by the machine to distribute N pennies. From the example above, the machine requires four boxes and seven iterations to distribute nine pennies.\r\n  ","description_html":"\u003cp\u003eA machine consists of a row of boxes. To start, one places N pennies in the leftmost box. The machine then redistributes the pennies as follows:\u003c/p\u003e\u003cp\u003eOn each iteration, it replaces a pair of pennies in one box with a single penny in the next box to the right. The iterations stop when there is no box with more than one coin. For example, the figure below shows the working of the machine in distributing nine pennies by always selecting a pair of pennies in the leftmost box with at least two coins.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eItr 0:   9  0  0  0        \r\nItr 1:   7  1  0  0 \r\nItr 2:   5  2  0  0  \r\nItr 3:   3  3  0  0  \r\nItr 4:   1  4  0  0   \r\nItr 5:   1  2  1  0   \r\nItr 6:   1  0  2  0   \r\nItr 7:   1  0  0  1  \r\n\u003c/pre\u003e\u003cp\u003eDetermine the number of boxes and iterations needed by the machine to distribute N pennies. From the example above, the machine requires four boxes and seven iterations to distribute nine pennies.\u003c/p\u003e","function_template":"function [box, itr] = PDMachine(N)\r\n \r\nend","test_suite":"%%\r\nN = 1;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,1) \u0026 isequal(itr,0))\r\n\r\n%%\r\nN = 2;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,2) \u0026 isequal(itr,1))\r\n\r\n%%\r\nN = 3;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,2) \u0026 isequal(itr,1))\r\n\r\n%%\r\nN = 5;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,3) \u0026 isequal(itr,3))\r\n\r\n%%\r\nN = 10;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,4) \u0026 isequal(itr,8))\r\n\r\n%%\r\nN = 19;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,5) \u0026 isequal(itr,16))\r\n\r\n%%\r\nN = 25;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,5) \u0026 isequal(itr,22))\r\n\r\n%%\r\nN = 50;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,6) \u0026 isequal(itr,47))\r\n\r\n%%\r\nN = 100;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,7) \u0026 isequal(itr,97))\r\n\r\n%%\r\nN = 777;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,10) \u0026 isequal(itr,773))\r\n\r\n%%\r\nN = 1234;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,11) \u0026 isequal(itr,1229))\r\n\r\n%%\r\nN = 5000;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,13) \u0026 isequal(itr,4995))\r\n\r\n%%\r\nN = 9999;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,14) \u0026 isequal(itr,9991))\r\n\r\n%%\r\nN = 100000;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,17) \u0026 isequal(itr,99994))\r\n\r\n%%\r\nN = 1234567;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,21) \u0026 isequal(itr,1234556))\r\n\r\n%%\r\nN = 12345678;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,24) \u0026 isequal(itr,12345666))\r\n\r\n%%\r\nN = 987654321;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,30) \u0026 isequal(itr,987654304))\r\n\r\n%%\r\nN = 1234567890;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,31) \u0026 isequal(itr,1234567878))\r\n\r\n%%\r\nN = 9876543210;\r\n[box, itr] = PDMachine(N);\r\nassert(isequal(box,34) \u0026 isequal(itr,9876543195))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":178544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":"2018-09-18T17:45:21.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-08-05T02:30:50.000Z","updated_at":"2025-12-05T12:14:33.000Z","published_at":"2018-08-05T03:02:52.000Z","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\u003eA machine consists of a row of boxes. To start, one places N pennies in the leftmost box. The machine then redistributes the pennies as follows:\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\u003eOn each iteration, it replaces a pair of pennies in one box with a single penny in the next box to the right. The iterations stop when there is no box with more than one coin. For example, the figure below shows the working of the machine in distributing nine pennies by always selecting a pair of pennies in the leftmost box with at least two coins.\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[Itr 0:   9  0  0  0        \\nItr 1:   7  1  0  0 \\nItr 2:   5  2  0  0  \\nItr 3:   3  3  0  0  \\nItr 4:   1  4  0  0   \\nItr 5:   1  2  1  0   \\nItr 6:   1  0  2  0   \\nItr 7:   1  0  0  1]]\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\u003eDetermine the number of boxes and iterations needed by the machine to distribute N pennies. From the example above, the machine requires four boxes and seven iterations to distribute nine pennies.\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:\"distribution 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