{"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":53004,"title":"Collect a set of candy wrappers","description":"This past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) their many neighbors with their costumes inspired by “mundane Halloween”, a Japanese tradition started in 2014. As they sifted through and sampled the candy they collected, they noticed something odd as they opened one type of candy, an Oh Leonhard! bar:\r\n“This wrapper has a proof of the infinitude of primes!”, said Matilda.\r\n“I got that one too,” said Labrun. “And here’s one with the Twin Prime Conjecture!”\r\n“Here’s the Pythagorean Theorem. And this one has the Riemann hypothesis.”\r\nThe precocious pair determined that these wrappers were part of the Oh Leonhard! “Great Theorems and Unsolved Problems” promotion. In this promotion, wrappers with one of forty theorems, conjectures, or other famous math problems were distributed evenly among all of the Oh Leonhard! Bars produces. Anyone who collected all wrappers in the set would get a copy of the Handbook of Mathematical Functions by Abramowitz and Stegun. \r\nMatilda and Labrun computed that, on average, they would have to open 172 wrappers to complete a set and win the prize. Their calculation accounted for the contest’s rule that all pieces of the wrapper had to be submitted—that is, no fractional wrappers were allowed.\r\nWrite a function that takes the number of wrappers in a set and compute the expected number of wrappers that would need to be opened to collect the set.","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: 369px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 184.5px; transform-origin: 407px 184.5px; 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: 276.975px 8.05px; transform-origin: 276.975px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51251\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003etheir many neighbors\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: 31.8917px 8.05px; transform-origin: 31.8917px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with their costumes inspired by “\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.spoon-tamago.com/2021/11/01/japan-jimi-mundane-halloween-2021/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003emundane Halloween\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: 244.658px 8.05px; transform-origin: 244.658px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e”, a Japanese tradition started in 2014. As they sifted through and sampled the candy they collected, they noticed something odd as they opened one type of candy, an Oh Leonhard! bar:\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: 207.317px 8.05px; transform-origin: 207.317px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e“This wrapper has a proof of the infinitude of primes!”, said Matilda.\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: 253.475px 8.05px; transform-origin: 253.475px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e“I got that one too,” said Labrun. “And here’s one with the Twin Prime Conjecture!”\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: 242.983px 8.05px; transform-origin: 242.983px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e“Here’s the Pythagorean Theorem. And this one has the Riemann hypothesis.”\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; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; 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: 359.025px 8.05px; transform-origin: 359.025px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe precocious pair determined that these wrappers were part of the Oh Leonhard! “Great Theorems and Unsolved Problems” promotion. In this promotion, wrappers with one of forty theorems, conjectures, or other famous math problems were distributed evenly among all of the Oh Leonhard! Bars produces. Anyone who collected all wrappers in the set would get a copy of 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: 117.475px 8.05px; transform-origin: 117.475px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e Handbook of Mathematical Functions\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: 89.4583px 8.05px; transform-origin: 89.4583px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by Abramowitz and Stegun. \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: 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: 383.15px 8.05px; transform-origin: 383.15px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMatilda and Labrun computed that, on average, they would have to open 172 wrappers to complete a set and win the prize. Their calculation accounted for the contest’s rule that all pieces of the wrapper had to be submitted—that is, no fractional wrappers were allowed.\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: 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: 383px 8.05px; transform-origin: 383px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the number of wrappers in a set and compute the expected number of wrappers that would need to be opened to collect the set.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = collectWrappers(n)\r\n  y = factorial(factorial(n));","test_suite":"%%\r\nn = 5;\r\ny_correct = 12;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 25;\r\ny_correct = 96;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 40;\r\ny_correct = 172;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 250;\r\ny_correct = 1526;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 500;\r\ny_correct = 3397;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 1000:25:1125;\r\ny_correct = [7486 7698 7911 8125 8339 8554];\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 2500;\r\ny_correct = 21004;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 10000;\r\ny_correct = 97877;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 250000;\r\ny_correct = 3251609;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 5e6;\r\ny_correct = 80010822;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 2.5e7;\r\ny_correct = 440290052;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 5e8;\r\ny_correct = 10303667162;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 2.5e9;\r\ny_correct = 55541930585;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%% Anti-lookup\r\nn = [7 17 71 77 117 171 177 711 717 771 777];\r\nyy_correct = [68 276 2216 2478 4393 7308 7647 46281 46777 51268 51779];\r\nindx = randi(11,[1 randi(11)]);\r\nassert(isequal(collectWrappers(collectWrappers(n(indx))),yy_correct(indx)))\r\n\r\n%%\r\nfiletext = fileread('collectWrappers.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2021-11-06T13:42:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-11-06T13:09:20.000Z","updated_at":"2026-01-02T17:08:42.000Z","published_at":"2021-11-06T13:12:12.000Z","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\u003eThis past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51251\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etheir many neighbors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e with their costumes inspired by “\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.spoon-tamago.com/2021/11/01/japan-jimi-mundane-halloween-2021/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emundane Halloween\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e”, a Japanese tradition started in 2014. As they sifted through and sampled the candy they collected, they noticed something odd as they opened one type of candy, an Oh Leonhard! bar:\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“This wrapper has a proof of the infinitude of primes!”, said Matilda.\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“I got that one too,” said Labrun. “And here’s one with the Twin Prime Conjecture!”\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“Here’s the Pythagorean Theorem. And this one has the Riemann hypothesis.”\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 precocious pair determined that these wrappers were part of the Oh Leonhard! “Great Theorems and Unsolved Problems” promotion. In this promotion, wrappers with one of forty theorems, conjectures, or other famous math problems were distributed evenly among all of the Oh Leonhard! Bars produces. Anyone who collected all wrappers in the set would get a copy of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e Handbook of Mathematical Functions\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by Abramowitz and Stegun. \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\u003eMatilda and Labrun computed that, on average, they would have to open 172 wrappers to complete a set and win the prize. Their calculation accounted for the contest’s rule that all pieces of the wrapper had to be submitted—that is, no fractional wrappers were allowed.\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 takes the number of wrappers in a set and compute the expected number of wrappers that would need to be opened to collect the set.\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":53004,"title":"Collect a set of candy wrappers","description":"This past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) their many neighbors with their costumes inspired by “mundane Halloween”, a Japanese tradition started in 2014. As they sifted through and sampled the candy they collected, they noticed something odd as they opened one type of candy, an Oh Leonhard! bar:\r\n“This wrapper has a proof of the infinitude of primes!”, said Matilda.\r\n“I got that one too,” said Labrun. “And here’s one with the Twin Prime Conjecture!”\r\n“Here’s the Pythagorean Theorem. And this one has the Riemann hypothesis.”\r\nThe precocious pair determined that these wrappers were part of the Oh Leonhard! “Great Theorems and Unsolved Problems” promotion. In this promotion, wrappers with one of forty theorems, conjectures, or other famous math problems were distributed evenly among all of the Oh Leonhard! Bars produces. Anyone who collected all wrappers in the set would get a copy of the Handbook of Mathematical Functions by Abramowitz and Stegun. \r\nMatilda and Labrun computed that, on average, they would have to open 172 wrappers to complete a set and win the prize. Their calculation accounted for the contest’s rule that all pieces of the wrapper had to be submitted—that is, no fractional wrappers were allowed.\r\nWrite a function that takes the number of wrappers in a set and compute the expected number of wrappers that would need to be opened to collect the set.","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: 369px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 184.5px; transform-origin: 407px 184.5px; 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: 276.975px 8.05px; transform-origin: 276.975px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51251\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003etheir many neighbors\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: 31.8917px 8.05px; transform-origin: 31.8917px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with their costumes inspired by “\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.spoon-tamago.com/2021/11/01/japan-jimi-mundane-halloween-2021/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003emundane Halloween\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: 244.658px 8.05px; transform-origin: 244.658px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e”, a Japanese tradition started in 2014. As they sifted through and sampled the candy they collected, they noticed something odd as they opened one type of candy, an Oh Leonhard! bar:\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: 207.317px 8.05px; transform-origin: 207.317px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e“This wrapper has a proof of the infinitude of primes!”, said Matilda.\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: 253.475px 8.05px; transform-origin: 253.475px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e“I got that one too,” said Labrun. “And here’s one with the Twin Prime Conjecture!”\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: 242.983px 8.05px; transform-origin: 242.983px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e“Here’s the Pythagorean Theorem. And this one has the Riemann hypothesis.”\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; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; 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: 359.025px 8.05px; transform-origin: 359.025px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe precocious pair determined that these wrappers were part of the Oh Leonhard! “Great Theorems and Unsolved Problems” promotion. In this promotion, wrappers with one of forty theorems, conjectures, or other famous math problems were distributed evenly among all of the Oh Leonhard! Bars produces. Anyone who collected all wrappers in the set would get a copy of 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: 117.475px 8.05px; transform-origin: 117.475px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e Handbook of Mathematical Functions\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: 89.4583px 8.05px; transform-origin: 89.4583px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by Abramowitz and Stegun. \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: 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: 383.15px 8.05px; transform-origin: 383.15px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMatilda and Labrun computed that, on average, they would have to open 172 wrappers to complete a set and win the prize. Their calculation accounted for the contest’s rule that all pieces of the wrapper had to be submitted—that is, no fractional wrappers were allowed.\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: 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: 383px 8.05px; transform-origin: 383px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the number of wrappers in a set and compute the expected number of wrappers that would need to be opened to collect the set.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = collectWrappers(n)\r\n  y = factorial(factorial(n));","test_suite":"%%\r\nn = 5;\r\ny_correct = 12;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 25;\r\ny_correct = 96;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 40;\r\ny_correct = 172;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 250;\r\ny_correct = 1526;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 500;\r\ny_correct = 3397;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 1000:25:1125;\r\ny_correct = [7486 7698 7911 8125 8339 8554];\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 2500;\r\ny_correct = 21004;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 10000;\r\ny_correct = 97877;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 250000;\r\ny_correct = 3251609;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 5e6;\r\ny_correct = 80010822;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 2.5e7;\r\ny_correct = 440290052;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 5e8;\r\ny_correct = 10303667162;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 2.5e9;\r\ny_correct = 55541930585;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%% Anti-lookup\r\nn = [7 17 71 77 117 171 177 711 717 771 777];\r\nyy_correct = [68 276 2216 2478 4393 7308 7647 46281 46777 51268 51779];\r\nindx = randi(11,[1 randi(11)]);\r\nassert(isequal(collectWrappers(collectWrappers(n(indx))),yy_correct(indx)))\r\n\r\n%%\r\nfiletext = fileread('collectWrappers.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2021-11-06T13:42:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-11-06T13:09:20.000Z","updated_at":"2026-01-02T17:08:42.000Z","published_at":"2021-11-06T13:12:12.000Z","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\u003eThis past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51251\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etheir many neighbors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e with their costumes inspired by “\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.spoon-tamago.com/2021/11/01/japan-jimi-mundane-halloween-2021/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emundane Halloween\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e”, a Japanese tradition started in 2014. As they sifted through and sampled the candy they collected, they noticed something odd as they opened one type of candy, an Oh Leonhard! bar:\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“This wrapper has a proof of the infinitude of primes!”, said Matilda.\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“I got that one too,” said Labrun. “And here’s one with the Twin Prime Conjecture!”\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“Here’s the Pythagorean Theorem. And this one has the Riemann hypothesis.”\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 precocious pair determined that these wrappers were part of the Oh Leonhard! “Great Theorems and Unsolved Problems” promotion. In this promotion, wrappers with one of forty theorems, conjectures, or other famous math problems were distributed evenly among all of the Oh Leonhard! Bars produces. Anyone who collected all wrappers in the set would get a copy of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e Handbook of Mathematical Functions\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by Abramowitz and Stegun. \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\u003eMatilda and Labrun computed that, on average, they would have to open 172 wrappers to complete a set and win the prize. Their calculation accounted for the contest’s rule that all pieces of the wrapper had to be submitted—that is, no fractional wrappers were allowed.\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 takes the number of wrappers in a set and compute the expected number of wrappers that would need to be opened to collect the 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