Problem 54775. Flip the parity of digits in a decimal expansion

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>The number 349 has the decimal expansion </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=\"3*100+4*10+9*1\"/></w:customXmlPr><w:r><w:t>3\\times 10^2 + 4\\times 10^1 + 9\\times 10^0</w:t></w:r></w:customXml><w:r><w:t>. If we change the even digits from positive to negative, then the number becomes 269 (i.e., 300-40+9). A similar operation could be applied to the odd digits. </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 a number </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=\"n\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> and produces two arrays: a vector </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=\"a\"/></w:customXmlPr><w:r><w:t>a</w:t></w:r></w:customXml><w:r><w:t> with the even digits of 1 to </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=\"n\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> with flipped parity and a vector </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=\"b\"/></w:customXmlPr><w:r><w:t>b</w:t></w:r></w:customXml><w:r><w:t> with the odd digits of 1 to </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=\"n\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> with flipped parity. </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>At first these sequences did not seem interesting, but plotting them--using </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>plot(a,1:n,b,1:n)</w:t></w:r><w:r><w:t> with </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=\"n = 10^4\"/></w:customXmlPr><w:r><w:t>n = 10^4</w:t></w:r></w:customXml><w:r><w:t>, say—convinced me that they are.</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: 144px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 72px; transform-origin: 407px 72px; 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: 138.1px 8px; transform-origin: 138.1px 8px; unicode-bidi: normal; ">The number 349 has the decimal expansion <img src="data:image/png;base64,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" alt="3*100+4*10+9*1" style="width: 168px; height: 19px;" width="168" height="19"><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: 141.958px 8px; transform-origin: 141.958px 8px; unicode-bidi: normal; ">. If we change the even digits from positive to negative, then the number becomes 269 (i.e., 300-40+9). A similar operation could be applied to the odd digits. </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: 114.217px 8px; transform-origin: 114.217px 8px; unicode-bidi: normal; ">Write a function that takes a number 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: 109.292px 8px; transform-origin: 109.292px 8px; unicode-bidi: normal; "> and produces two arrays: a vector 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: 84.7833px 8px; transform-origin: 84.7833px 8px; unicode-bidi: normal; "> with the even digits of 1 to 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: 57.9583px 8px; transform-origin: 57.9583px 8px; unicode-bidi: normal; "> with flipped parity and a vector b<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: 81.2833px 8px; transform-origin: 81.2833px 8px; unicode-bidi: normal; "> with the odd digits of 1 to 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: 59.3833px 8px; transform-origin: 59.3833px 8px; unicode-bidi: normal; "> with flipped parity. </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: 229.875px 8px; transform-origin: 229.875px 8px; unicode-bidi: normal; ">At first these sequences did not seem interesting, but plotting them--using <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: 65.45px 8px; transform-origin: 65.45px 8px; unicode-bidi: normal; ">plot(a,1:n,b,1: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: 16.3333px 8px; transform-origin: 16.3333px 8px; unicode-bidi: normal; "> with <img src="data:image/png;base64,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" alt="n = 10^4" style="width: 49px; height: 19px;" width="49" height="19"><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: 21.775px 8px; transform-origin: 21.775px 8px; unicode-bidi: normal; ">, say—convinced me that they are.</div></div></div>

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Problem 54775. Flip the parity of digits in a decimal expansion

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Problem 54775. Flip the parity of digits in a decimal expansion

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