{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":60968,"title":"Monkey and the Peaches","description":"A monkey picked a certain number of peaches on the first day.\r\nEach day, the monkey eats half of the remaining peaches plus one more. This continues every day.\r\nOn the x-th morning, the monkey finds only 1 peach remaining before eating.\r\nWrite a function that returns the number of peaches the monkey must have picked on day 1, given x, the number of days this routine lasted.","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: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 66px; transform-origin: 408px 66px; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA monkey picked a certain number of peaches on the first day.\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach day, the monkey eats \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ehalf of the remaining peaches plus one more\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. This continues every day.\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex-th morning\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the monkey finds only \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e1 peach\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e remaining before eating.\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the number of peaches the monkey must have picked on day 1, given \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the number of days this routine lasted.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function totalPeaches = monkeyPeachDayOne(x)\r\n  totalPeaches = 1;\r\nend","test_suite":"%%\r\nassert(isequal(monkeyPeachDayOne(1), 1))\r\n%%\r\nassert(isequal(monkeyPeachDayOne(2), 4))\r\n%%\r\n% On 3rd morning: 1 peach left\r\nassert(isequal(monkeyPeachDayOne(3), 10))\r\n%%\r\nassert(isequal(monkeyPeachDayOne(5), 46))\r\n%%\r\nassert(isequal(monkeyPeachDayOne(10), 1534))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":4915547,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-18T20:29:03.000Z","updated_at":"2025-10-01T15:21:29.000Z","published_at":"2025-07-18T20:29:03.000Z","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\u003eA monkey picked a certain number of peaches on the first day.\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\u003eEach day, the monkey eats \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ehalf of the remaining peaches plus one more\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. This continues every day.\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 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex-th morning\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the monkey finds only \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1 peach\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e remaining before eating.\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 that returns the number of peaches the monkey must have picked on day 1, given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the number of days this routine lasted.\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":1512,"title":"Clock Solitaire","description":"Many card players will be familiar with the game of  \u003chttp://en.wikipedia.org/wiki/Clock_patience Clock Solitaire\u003e.  Briefly, the player sets up by creating thirteen piles of four face-down cards at random, each associated with one of the ranks ace through king.  Beginning with the top card in the king's pile, the player places the drawn card face up beneath its home pile, and draws a new card from the top of that same pile.  Play continues until the fourth king is drawn.  If all cards are face up in their home piles at this time, the game is a winner.\r\n\r\nSince clock solitaire is a purely deterministic game, a computer can easily be programmed to play.  For this problem, you will write a function that takes a deck and reports whether or not it is a winning configuration.  More specifically, the input will be some permutation of the integers 1:52, where 1:13 represent the ace through king of clubs, 14:26 the ace through king of diamonds, 27:39 the hearts, and 40:52 the spades.  Assume that the cards are formed into 13 piles by taking the first four cards as the ace pile, next four as the deuce pile, etc.  Output is a single scalar boolean indicating whether the game will be won using this deck.\r\n\r\nArmed with this function, one can determine empirically what the win rate is for randomly shuffled decks.  See if you can find out!","description_html":"\u003cp\u003eMany card players will be familiar with the game of  \u003ca href = \"http://en.wikipedia.org/wiki/Clock_patience\"\u003eClock Solitaire\u003c/a\u003e.  Briefly, the player sets up by creating thirteen piles of four face-down cards at random, each associated with one of the ranks ace through king.  Beginning with the top card in the king's pile, the player places the drawn card face up beneath its home pile, and draws a new card from the top of that same pile.  Play continues until the fourth king is drawn.  If all cards are face up in their home piles at this time, the game is a winner.\u003c/p\u003e\u003cp\u003eSince clock solitaire is a purely deterministic game, a computer can easily be programmed to play.  For this problem, you will write a function that takes a deck and reports whether or not it is a winning configuration.  More specifically, the input will be some permutation of the integers 1:52, where 1:13 represent the ace through king of clubs, 14:26 the ace through king of diamonds, 27:39 the hearts, and 40:52 the spades.  Assume that the cards are formed into 13 piles by taking the first four cards as the ace pile, next four as the deuce pile, etc.  Output is a single scalar boolean indicating whether the game will be won using this deck.\u003c/p\u003e\u003cp\u003eArmed with this function, one can determine empirically what the win rate is for randomly shuffled decks.  See if you can find out!\u003c/p\u003e","function_template":"function isWinner = clockSolitaire(deck)\r\n  isWinner = true;\r\nend","test_suite":"%%\r\ndeck = [1:52];\r\nassert(isequal(clockSolitaire(deck),false))\r\n\r\n%%\r\ndeck = [8 1 5 2 30 23 46 21 3 51 6 27 42 48 37 33 12 25 45 36 31 34 29 35 15 17 43 13 39 40 18 50 26 9 4 28 38 16 11 22 49 24 14 7 32 20 47 44 19 10 41 52];\r\nassert(isequal(clockSolitaire(deck),true))\r\n%%\r\ndeck = [52:-1:1];\r\nassert(isequal(clockSolitaire(deck),false))\r\n\r\n%%\r\ndeck = [40 29 25 37 23 41 13 50 33 2 42 20 49 48 27 46 36 45 28 1 7 11 14 5 9 26 15 21 12 8 19 35 10 38 34 52 32 51 31 16 18 22 6 3 47 44 43 4 24 17 30 39];\r\nassert(isequal(clockSolitaire(deck),true))\r\n\r\n%%\r\ndeck = [40 29 25 37 23 41 13 50 33 2 42 20 52 48 27 46 36 45 28 1 7 11 14 5 9 26 15 21 12 8 19 35 10 38 34 49 32 51 31 16 18 22 6 3 47 44 43 4 24 17 30 39];\r\nassert(isequal(clockSolitaire(deck),false))\r\n\r\n%%\r\ndeck = [8 1 5 2 30 23 46 21 3 51 6 27 13 48 37 33 12 25 45 36 31 34 29 35 15 17 43 42 39 40 18 50 26 9 4 28 38 16 11 22 49 24 14 7 32 20 47 44 19 10 41 52];\r\nassert(isequal(clockSolitaire(deck),false))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":3117,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":15,"created_at":"2013-05-16T01:27:06.000Z","updated_at":"2026-02-15T04:05:23.000Z","published_at":"2013-05-16T01:27:05.000Z","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\u003eMany card players will be familiar with the game of \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://en.wikipedia.org/wiki/Clock_patience\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eClock Solitaire\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Briefly, the player sets up by creating thirteen piles of four face-down cards at random, each associated with one of the ranks ace through king. Beginning with the top card in the king's pile, the player places the drawn card face up beneath its home pile, and draws a new card from the top of that same pile. Play continues until the fourth king is drawn. If all cards are face up in their home piles at this time, the game is a winner.\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\u003eSince clock solitaire is a purely deterministic game, a computer can easily be programmed to play. For this problem, you will write a function that takes a deck and reports whether or not it is a winning configuration. More specifically, the input will be some permutation of the integers 1:52, where 1:13 represent the ace through king of clubs, 14:26 the ace through king of diamonds, 27:39 the hearts, and 40:52 the spades. Assume that the cards are formed into 13 piles by taking the first four cards as the ace pile, next four as the deuce pile, etc. Output is a single scalar boolean indicating whether the game will be won using this deck.\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\u003eArmed with this function, one can determine empirically what the win rate is for randomly shuffled decks. See if you can find out!\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":60968,"title":"Monkey and the Peaches","description":"A monkey picked a certain number of peaches on the first day.\r\nEach day, the monkey eats half of the remaining peaches plus one more. This continues every day.\r\nOn the x-th morning, the monkey finds only 1 peach remaining before eating.\r\nWrite a function that returns the number of peaches the monkey must have picked on day 1, given x, the number of days this routine lasted.","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: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 66px; transform-origin: 408px 66px; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA monkey picked a certain number of peaches on the first day.\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach day, the monkey eats \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ehalf of the remaining peaches plus one more\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. This continues every day.\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex-th morning\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the monkey finds only \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e1 peach\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e remaining before eating.\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the number of peaches the monkey must have picked on day 1, given \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the number of days this routine lasted.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function totalPeaches = monkeyPeachDayOne(x)\r\n  totalPeaches = 1;\r\nend","test_suite":"%%\r\nassert(isequal(monkeyPeachDayOne(1), 1))\r\n%%\r\nassert(isequal(monkeyPeachDayOne(2), 4))\r\n%%\r\n% On 3rd morning: 1 peach left\r\nassert(isequal(monkeyPeachDayOne(3), 10))\r\n%%\r\nassert(isequal(monkeyPeachDayOne(5), 46))\r\n%%\r\nassert(isequal(monkeyPeachDayOne(10), 1534))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":4915547,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-18T20:29:03.000Z","updated_at":"2025-10-01T15:21:29.000Z","published_at":"2025-07-18T20:29:03.000Z","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\u003eA monkey picked a certain number of peaches on the first day.\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\u003eEach day, the monkey eats \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ehalf of the remaining peaches plus one more\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. This continues every day.\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 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex-th morning\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the monkey finds only \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1 peach\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e remaining before eating.\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 that returns the number of peaches the monkey must have picked on day 1, given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the number of days this routine lasted.\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":1512,"title":"Clock Solitaire","description":"Many card players will be familiar with the game of  \u003chttp://en.wikipedia.org/wiki/Clock_patience Clock Solitaire\u003e.  Briefly, the player sets up by creating thirteen piles of four face-down cards at random, each associated with one of the ranks ace through king.  Beginning with the top card in the king's pile, the player places the drawn card face up beneath its home pile, and draws a new card from the top of that same pile.  Play continues until the fourth king is drawn.  If all cards are face up in their home piles at this time, the game is a winner.\r\n\r\nSince clock solitaire is a purely deterministic game, a computer can easily be programmed to play.  For this problem, you will write a function that takes a deck and reports whether or not it is a winning configuration.  More specifically, the input will be some permutation of the integers 1:52, where 1:13 represent the ace through king of clubs, 14:26 the ace through king of diamonds, 27:39 the hearts, and 40:52 the spades.  Assume that the cards are formed into 13 piles by taking the first four cards as the ace pile, next four as the deuce pile, etc.  Output is a single scalar boolean indicating whether the game will be won using this deck.\r\n\r\nArmed with this function, one can determine empirically what the win rate is for randomly shuffled decks.  See if you can find out!","description_html":"\u003cp\u003eMany card players will be familiar with the game of  \u003ca href = \"http://en.wikipedia.org/wiki/Clock_patience\"\u003eClock Solitaire\u003c/a\u003e.  Briefly, the player sets up by creating thirteen piles of four face-down cards at random, each associated with one of the ranks ace through king.  Beginning with the top card in the king's pile, the player places the drawn card face up beneath its home pile, and draws a new card from the top of that same pile.  Play continues until the fourth king is drawn.  If all cards are face up in their home piles at this time, the game is a winner.\u003c/p\u003e\u003cp\u003eSince clock solitaire is a purely deterministic game, a computer can easily be programmed to play.  For this problem, you will write a function that takes a deck and reports whether or not it is a winning configuration.  More specifically, the input will be some permutation of the integers 1:52, where 1:13 represent the ace through king of clubs, 14:26 the ace through king of diamonds, 27:39 the hearts, and 40:52 the spades.  Assume that the cards are formed into 13 piles by taking the first four cards as the ace pile, next four as the deuce pile, etc.  Output is a single scalar boolean indicating whether the game will be won using this deck.\u003c/p\u003e\u003cp\u003eArmed with this function, one can determine empirically what the win rate is for randomly shuffled decks.  See if you can find out!\u003c/p\u003e","function_template":"function isWinner = clockSolitaire(deck)\r\n  isWinner = true;\r\nend","test_suite":"%%\r\ndeck = [1:52];\r\nassert(isequal(clockSolitaire(deck),false))\r\n\r\n%%\r\ndeck = [8 1 5 2 30 23 46 21 3 51 6 27 42 48 37 33 12 25 45 36 31 34 29 35 15 17 43 13 39 40 18 50 26 9 4 28 38 16 11 22 49 24 14 7 32 20 47 44 19 10 41 52];\r\nassert(isequal(clockSolitaire(deck),true))\r\n%%\r\ndeck = [52:-1:1];\r\nassert(isequal(clockSolitaire(deck),false))\r\n\r\n%%\r\ndeck = [40 29 25 37 23 41 13 50 33 2 42 20 49 48 27 46 36 45 28 1 7 11 14 5 9 26 15 21 12 8 19 35 10 38 34 52 32 51 31 16 18 22 6 3 47 44 43 4 24 17 30 39];\r\nassert(isequal(clockSolitaire(deck),true))\r\n\r\n%%\r\ndeck = [40 29 25 37 23 41 13 50 33 2 42 20 52 48 27 46 36 45 28 1 7 11 14 5 9 26 15 21 12 8 19 35 10 38 34 49 32 51 31 16 18 22 6 3 47 44 43 4 24 17 30 39];\r\nassert(isequal(clockSolitaire(deck),false))\r\n\r\n%%\r\ndeck = [8 1 5 2 30 23 46 21 3 51 6 27 13 48 37 33 12 25 45 36 31 34 29 35 15 17 43 42 39 40 18 50 26 9 4 28 38 16 11 22 49 24 14 7 32 20 47 44 19 10 41 52];\r\nassert(isequal(clockSolitaire(deck),false))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":3117,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":15,"created_at":"2013-05-16T01:27:06.000Z","updated_at":"2026-02-15T04:05:23.000Z","published_at":"2013-05-16T01:27:05.000Z","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\u003eMany card players will be familiar with the game of \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://en.wikipedia.org/wiki/Clock_patience\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eClock Solitaire\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Briefly, the player sets up by creating thirteen piles of four face-down cards at random, each associated with one of the ranks ace through king. Beginning with the top card in the king's pile, the player places the drawn card face up beneath its home pile, and draws a new card from the top of that same pile. Play continues until the fourth king is drawn. If all cards are face up in their home piles at this time, the game is a winner.\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\u003eSince clock solitaire is a purely deterministic game, a computer can easily be programmed to play. For this problem, you will write a function that takes a deck and reports whether or not it is a winning configuration. More specifically, the input will be some permutation of the integers 1:52, where 1:13 represent the ace through king of clubs, 14:26 the ace through king of diamonds, 27:39 the hearts, and 40:52 the spades. Assume that the cards are formed into 13 piles by taking the first four cards as the ace pile, next four as the deuce pile, etc. Output is a single scalar boolean indicating whether the game will be won using this deck.\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\u003eArmed with this function, one can determine empirically what the win rate is for randomly shuffled decks. 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