Problem 52849. Easy Sequences 34: Modified Pascal's Triangle

Created by Ramon Villamangca

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>Consider the integer triangle below:</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:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"158\"/><w:attr w:name=\"width\" w:val=\"167\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>It follows the same rule as </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Pascal's_triangle\"><w:r><w:t>Pascal's Triangle</w:t></w:r></w:hyperlink><w:r><w:t>, except that instead of affixing 1's at the sides of each row, the row number minus 1, is affixed (on first row 0 is affixed; at row 2, 1 is affixed on each side, etc.). Any inner number, as in Pascal's Triangle, is the sum of the left and right numbers on its previous row. </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:rPr><w:b/></w:rPr><w:t>Given a number </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:rPr><w:b/></w:rPr><w:t> find </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>S(n)</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, which is the sum of the n-th row.</w:t></w:r><w:r><w:t> Hence, </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>S(1)=0</w:t></w:r></w:customXml><w:r><w:t> and </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>S(4)=14</w:t></w:r></w:customXml><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>We could be getting large numbers here, therefore please </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>concatenate the total number of digits with the last 3 digits 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>S(n)</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> and output a single concatenated integer. </w:t></w:r><w:r><w:t>For example the </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>S(5) = 30</w:t></w:r></w:customXml><w:r><w:t>, hence the output should be </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>2030</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.png","relationshipId":"rId1"}]},{"partUri":"/media/image1.png","contentType":"image/png","content":"data:image/png;base64,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","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: 20.440000534057617px; 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: normal; text-decoration: none; white-space: normal; "><div style="block-size: 347px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><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; text-align: left; 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; "><span style="">Consider the integer triangle below:</span></span></div><div style="block-size: 164px; 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; text-align: left; 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; "><span style="">                                                                    </span></span><img class="imageNode" width="167" height="158" style="vertical-align: baseline;width: 167px;height: 158px" src="data:image/png;base64,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" data-image-state="image-loaded"></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; text-align: left; 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; "><span style="">It follows the same rule as </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Pascal's_triangle"><span style=""><span style="">Pascal's Triangle</span></span></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; "><span style="">, except that instead of affixing 1's at the sides of each row, the row number minus 1, is affixed (on first row 0 is affixed; at row 2, 1 is affixed on each side, etc.). Any inner number, as in Pascal's Triangle, is the sum of the left and right numbers on its previous row. </span></span></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; text-align: left; 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; "><span style="font-weight: bold; ">Given a number </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">n</span><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; "><span style="font-weight: bold; "> find </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="30.5" height="19" style="width: 30.5px; height: 19px;"></span><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; "><span style="font-weight: bold; ">, which is the sum of the n-th row.</span></span><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; "><span style=""> Hence, </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="56.5" height="19" style="width: 56.5px; height: 19px;"></span><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; "><span style=""> and </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="64" height="19" style="width: 64px; height: 19px;"></span><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; "><span style="">. </span></span></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; text-align: left; 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; "><span style="">We could be getting large numbers here, therefore please </span></span><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; "><span style="font-weight: bold; ">concatenate the total number of digits with the last 3 digits of </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="30.5" height="19" style="width: 30.5px; height: 19px;"></span><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; "><span style="font-weight: bold; "> and output a single concatenated integer. </span></span><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; "><span style="">For example the </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="64" height="19" style="width: 64px; height: 19px;"></span><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; "><span style="">, hence the output should be </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEIAAAAkCAYAAAA9+eyvAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAQqADAAQAAAABAAAAJAAAAAD+3wP6AAAEb0lEQVRoBe2XW4hWVRTHP7OLI+bdyilk1LzLmFB5idIQlcQQCYwEYXzzISIEQX0ZtIfeUgh6SUESS0syH4xKEa+JIuStIlEYsjTFvKTVOKX5+3/fWbDc7vPdv57Ogt+3115r7b32rLPP3mdyuUyyCmQVyCqQVSCrQLkV6FYicDj+qdAKPeAwHIKzUEo092yYAs1wEr6C01BKBhAwB8ZBbzgKyvsjlJJa8t4390NY2qEL/ouwAVt3SJPHcBwDjb0EW+FK0v+Wti+kyWIcv0Ms71rsxR5eLXmj6/kwZSF+cduIeTgyuh+248n4XbQqquQR2A+a4wj0gVAWYpD/JmwB7aBr4PO2049JLXlj8+VmYlXiUzAD9Epo0bPgBPhFzaUfyl4MivkL9Gp5GUnnb5D/c+9AHwwa8w0MBBMV+22wvFpDTKrNG5srb/ua31/g8UhEE7YzYItaE8Q863ybAp91P05ibtO2mJF2NWinaOfE5HuMlvfRIKCWvPmpHggm7EV/OiyDixCKnuYqZ5zmdKmLXX+f071qduVe4hwqQBvccjav2np0ftz0DvRa8gZTFbq6HXZC96i3YBxPY0/mqIvTWWAHovyjnc+rY+nYeB2k5YiK9CdonHaUl0bm9Xnu05/GYn/Ip847zNm17bs5n1dll9/m0FVZSl4jQPG/wRNBcF3yantWKi1uwBdOf9Lpf6Br4TGR/YZzDHF6TJ2DcSNotz0HKoaXuuStphCvJqvQO+tP/ma3Ol15xcT70wqhJ/8uqNg6pPuDDuAwvi55Ky1ETxbyBkjegs68VvjxW/a6s8dUvyP0ERTKmxjOwXLQGWDyIspB0KFuUpe8lRaineyDQGeDPx+0KN0oJmnng/kfNIU2djCvx67DdhKoGP6WeIr+CjCpZ16bs2iru/ofOALaqqHMw6D3X3RAMenAabHziwUmvhZafaXamNOJXU0j87o0BVVP4Vc4C34rFryF38k0tlB/BvgY0+W3WI0rR/QR1QUa9y/oi1PS6LyFLPz2hu9AhRgKaaJi2R93Bz3ttZNdfosNDz9cqbIHj42za/f/yJt/BfaS/DKMhVJykgBb6ISU4FYXcyYlJs38TjL2ShBQc960p6Y8Oq23wkR4BX6AmLRhfD5xfOYCpjndqy+7zianl6PaLtAf7qVheVWgLaATeTqkyUs4OmFUEjCG1nbEtsQWNttdzIjQWaSvB6MdpPnDA7YheXX1rUsSnqfdEOEjbDo39Km8D7y8T0eLlU/Xn5epdGSXf713oL8O+njS1dgEoazEoHF7QkfSrzZvynS53Ht4lLBcFgUz6bvgy2S8Xid76iPRf0rsO2j9twTd/AeU5fyZfhsMBr2aH4B8uyH8FxxTXqrNa+PvaV+gZ4spp71KfOzpabGbwZ5+B7rmU/8T6AmhLMUQy6n/Ww7AAtBuLSbV5M3PV2riYknL8elq1O3RDBfgGOhpp4nOmmegH5yDU6B4FagSqTRvJXNnsVkFsgpkFcgqkFUgq0BWgXsqcBcixH9wGq9jFgAAAABJRU5ErkJggg==" width="33" height="18" style="width: 33px; height: 18px;"></span><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; "><span style="">.</span></span></div></div></div>

Solve

Solution Stats

9 Solutions
6 Solvers

Last Solution submitted on Oct 24, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers6

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 52849. Easy Sequences 34: Modified Pascal's Triangle

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers6

Suggested Problems

More from this Author90

Problem Tags

Community Treasure Hunt

Problem 52849. Easy Sequences 34: Modified Pascal's Triangle

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers6

Suggested Problems

More from this Author90

Problem Tags

Community Treasure Hunt

Players