Problem 51251. Locate a family on a long street

Created by ChrisR

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{"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>Two children, Matilda and Labrun, live on a street in which—unlike many streets in the U.S.—the houses on one side are numbered consecutively, starting at 1. They notice that the sum of the numbers on the houses to the left of theirs equals the sum of the numbers to the right. </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 that takes </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"nmax\"/></w:customXmlPr><w:r><w:t>n_{max}</w:t></w:r></w:customXml><w:r><w:t>, the maximum number of houses on the street, and returns the largest possible number of houses and the number of the house where the family of Matilda and Labrun lives. For example, if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"nmax\"/></w:customXmlPr><w:r><w:t>n_{max}</w:t></w:r></w:customXml><w:r><w:t> = 10, then the function should find that the street has 8 houses and Matilda and Labrun live in house 6 because 1+2+3+4+5 = 7+8 = 15.</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>Henry Dudeney posed a version of this problem in </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Strand Magazine</w:t></w:r><w:r><w:t> in the early part of the 20</w:t></w:r><w:r><w:t>th</w:t></w:r><w:r><w:t> century. Although the connections might not be immediately clear, you might try Cody Problems </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/groups/25/problems/1215\"><w:r><w:t>1215</w:t></w:r></w:hyperlink><w:r><w:t>, </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/8057\"><w:r><w:t>8057</w:t></w:r></w:hyperlink><w:r><w:t>, and </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/45253\"><w:r><w:t>45253</w:t></w:r></w:hyperlink><w:r><w:t> as well.</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: 186.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 93.25px; transform-origin: 407px 93.25px; vertical-align: baseline; "><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: 374.983px 7.91667px; transform-origin: 374.983px 7.91667px; unicode-bidi: normal; ">Two children, Matilda and Labrun, live on a street in which—unlike many streets in the U.S.—the houses on one side are numbered consecutively, starting at 1. They notice that the sum of the numbers on the houses to the left of theirs equals the sum of the numbers to the right. </div><div style="block-size: 63.5px; 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 31.75px; text-align: left; transform-origin: 384px 31.75px; 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: 82.7083px 7.91667px; transform-origin: 82.7083px 7.91667px; unicode-bidi: normal; ">Write a function that takes <img src="data:image/png;base64,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" alt="nmax" style="width: 27px; height: 20px;" width="27" height="20"><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: 281.6px 7.91667px; transform-origin: 281.6px 7.91667px; unicode-bidi: normal; ">, the maximum number of houses on the street, and returns the largest possible number of houses and the number of the house where the family of Matilda and Labrun lives. For example, if <img src="data:image/png;base64,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" alt="nmax" style="width: 27px; height: 20px;" width="27" height="20"><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: 46.8667px 7.91667px; transform-origin: 46.8667px 7.91667px; unicode-bidi: normal; "> = 10, then the function should find that the street has 8 houses and Matilda and Labrun live in house 6 because 1+2+3+4+5 = 7+8 = 15.</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: 157.158px 7.91667px; transform-origin: 157.158px 7.91667px; unicode-bidi: normal; ">Henry Dudeney posed a version of this problem in <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: 52.9083px 7.91667px; transform-origin: 52.9083px 7.91667px; unicode-bidi: normal; ">Strand Magazine<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: 79.3417px 7.91667px; transform-origin: 79.3417px 7.91667px; unicode-bidi: normal; "> in the early part of the 20<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: 5.83333px 7.91667px; transform-origin: 5.83333px 7.91667px; unicode-bidi: normal; ">th<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: 69.4917px 7.91667px; transform-origin: 69.4917px 7.91667px; unicode-bidi: normal; "> century. Although the connections might not be immediately clear, you might try Cody Problems <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/groups/25/problems/1215">1215</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: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; ">, <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/8057">8057</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: 17.5px 7.91667px; transform-origin: 17.5px 7.91667px; unicode-bidi: normal; ">, and <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/45253">45253</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: 25.2833px 7.91667px; transform-origin: 25.2833px 7.91667px; unicode-bidi: normal; "> as well.</div></div></div>

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ChrisR on 16 May 2021

Test added to discourage lookup solutions.

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Problem 51251. Locate a family on a long street

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Problem 51251. Locate a family on a long street

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