Problem 47518. Play Outside In with primes

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>In the word game Outside In,* you start with a word, take the first and last letters, try to think of a word in which the two letters appear together in the interior, and repeat. For example, starting with ‘MATLAB’, you might proceed as follows:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>so</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>mb</w:t></w:r><w:r><w:t>rero, dis</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>so</w:t></w:r><w:r><w:t>lution, ki</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>dn</w:t></w:r><w:r><w:t>ap, pic</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>kp</w:t></w:r><w:r><w:t>ocket, helico</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>pt</w:t></w:r><w:r><w:t>er, birt</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>hr</w:t></w:r><w:r><w:t>ight, de</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>bt</w:t></w:r><w:r><w:t>or, taw</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>dr</w:t></w:r><w:r><w:t>y, ka</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>ty</w:t></w:r><w:r><w:t>did, bac</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>kd</w:t></w:r><w:r><w:t>rop, su</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>bp</w:t></w:r><w:r><w:t>oena, anniver</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>sa</w:t></w:r><w:r><w:t>ry, p</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>ay</w:t></w:r><w:r><w:t>back, na</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>pk</w:t></w:r><w:r><w:t>in, tu</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>nn</w:t></w:r><w:r><w:t>el, ma</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>nn</w:t></w:r><w:r><w:t>equin, sole</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>mn</w:t></w:r><w:r><w:t>ity, p</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>sy</w:t></w:r><w:r><w:t>chosis, lo</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>ps</w:t></w:r><w:r><w:t>ided, ba</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>ld</w:t></w:r><w:r><w:t>erdash, etc. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>You can play alone or with others, and you could add other rules or objectives—e.g., all words must have six or more letters; a person who cannot think of a word is eliminated; players try to generate a list that uses all letters in the alphabet, etc. </w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:t> </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>This game has one problem: without a convenient and stable word list, it does not translate easily to Cody. So instead of words, let’s use prime numbers. In particular, start with a two-digit seed, find the smallest prime for which the two digits appear together in the interior, create a new two-digit number from the first and last digits of the prime, and repeat. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, if the seed is 11, then the list would start 1117, 1171, 2111, 1213, 2131, 1217,… Because </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/45994-investigate-the-frequency-of-last-digits-of-prime-numbers\"><w:r><w:t>the last digits of primes are constrained</w:t></w:r></w:hyperlink><w:r><w:t>, you will notice similarities in lists generated from different seeds. Solvers able to plot the numbers might enjoy seeing the patterns for longer lists graphically. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function to play Outside In with primes: given a two-digit seed </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x</w:t></w:r></w:customXml><w:r><w:t>, generate a list of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> primes following the rules above. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>*I devised the game and the name, but I would be surprised if someone had not already thought of it.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div 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; "><div style="block-size: 420px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 210px; transform-origin: 407px 210px; vertical-align: baseline; "><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.683px 7.91667px; transform-origin: 368.683px 7.91667px; unicode-bidi: normal; ">In the word game Outside In,* you start with a word, take the first and last letters, try to think of a word in which the two letters appear together in the interior, and repeat. For example, starting with ‘MATLAB’, you might proceed as follows:</div><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.39167px 7.91667px; transform-origin: 7.39167px 7.91667px; unicode-bidi: normal; ">so<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; 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margin-right: 0px; margin-top: 0px; perspective-origin: 33.85px 7.91667px; transform-origin: 33.85px 7.91667px; unicode-bidi: normal; ">equin, sole<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.5px 7.91667px; transform-origin: 10.5px 7.91667px; unicode-bidi: normal; ">mn<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.2583px 7.91667px; transform-origin: 14.2583px 7.91667px; unicode-bidi: normal; ">ity, p<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.78333px 7.91667px; transform-origin: 7.78333px 7.91667px; unicode-bidi: normal; ">sy<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.175px 7.91667px; transform-origin: 29.175px 7.91667px; unicode-bidi: normal; ">chosis, lo<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.16667px 7.91667px; transform-origin: 8.16667px 7.91667px; unicode-bidi: normal; ">ps<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.9px 7.91667px; transform-origin: 24.9px 7.91667px; unicode-bidi: normal; ">ided, ba<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.21667px 7.91667px; transform-origin: 6.21667px 7.91667px; unicode-bidi: normal; ">ld<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.5px 7.91667px; transform-origin: 38.5px 7.91667px; unicode-bidi: normal; ">erdash, etc. </div><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 363.05px 7.91667px; transform-origin: 363.05px 7.91667px; unicode-bidi: normal; ">You can play alone or with others, and you could add other rules or objectives—e.g., all words must have six or more letters; a person who cannot think of a word is eliminated; players try to generate a list that uses all letters in the alphabet, etc. <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; "> <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; "> </div><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373.283px 7.91667px; transform-origin: 373.283px 7.91667px; unicode-bidi: normal; ">This game has one problem: without a convenient and stable word list, it does not translate easily to Cody. So instead of words, let’s use prime numbers. In particular, start with a two-digit seed, find the smallest prime for which the two digits appear together in the interior, create a new two-digit number from the first and last digits of the prime, and repeat. </div><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 318.958px 7.91667px; transform-origin: 318.958px 7.91667px; unicode-bidi: normal; ">For example, if the seed is 11, then the list would start 1117, 1171, 2111, 1213, 2131, 1217,… Because <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/45994-investigate-the-frequency-of-last-digits-of-prime-numbers">the last digits of primes are constrained</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 306.775px 7.91667px; transform-origin: 306.775px 7.91667px; unicode-bidi: normal; ">, you will notice similarities in lists generated from different seeds. Solvers able to plot the numbers might enjoy seeing the patterns for longer lists graphically. </div><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 215.742px 7.91667px; transform-origin: 215.742px 7.91667px; unicode-bidi: normal; ">Write a function to play Outside In with primes: given a two-digit seed x<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.5583px 7.91667px; transform-origin: 57.5583px 7.91667px; unicode-bidi: normal; ">, generate a list of n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.8583px 7.91667px; transform-origin: 82.8583px 7.91667px; unicode-bidi: normal; "> primes following the rules above. </div><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-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 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; "></div><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.567px 7.91667px; transform-origin: 311.567px 7.91667px; unicode-bidi: normal; ">*I devised the game and the name, but I would be surprised if someone had not already thought of it.</div></div></div>

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Last Solution submitted on Nov 20, 2020

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Problem 47518. Play Outside In with primes

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Problem 47518. Play Outside In with primes

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