Problem 840. SET (the card game)

Created by Matthew Eicholtz

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:hyperlink w:docLocation=\"https://www.setgame.com/sites/default/files/instructions/SET%20INSTRUCTIONS%20-%20ENGLISH.pdf\"><w:r><w:t>SET</w:t></w:r></w:hyperlink><w:r><w:t> is a card game in which players try to find valid 3-card sets from 12 cards on the table. What makes a valid set? Every card has four features, each with three possible values. In a valid set, each of the features, when looked at individually, are either the</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>same</w:t></w:r><w:r><w:t> on each card OR</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>different</w:t></w:r><w:r><w:t> on each card.</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>In this problem, you are given a 12x4 matrix representing 12 cards (rows) with 4 features (columns) each. The</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>N</w:t></w:r><w:r><w:t>-th row corresponds to the</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>N</w:t></w:r><w:r><w:t>-th card. Each feature has a value of 0, 1, or 2. Create a function that returns an Mx3 matrix of all valid sets, where each row is a set and each column is the index to a card in the set. For every set, the cards (columns) should be arranged in ascending order. If there are no valid sets for a given input, return []. You may assume that all cards are unique.</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>Example</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[cards = [1 0 1 0\n         1 1 1 1\n         2 2 1 0\n         0 1 2 2\n         2 1 1 1\n         1 0 1 2\n         0 0 0 0\n         2 2 2 2\n         0 2 0 0\n         1 1 1 0\n         0 1 0 2\n         0 2 0 2];]]></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>returns</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[sets = [2 7 8\n        6 8 11]]]></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>because there are two valid sets. Cards 2,7, and 8 make one set and cards 6,8, and 11 form another set. Notice that a card can be a part of more than one set.</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: 20px; 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="display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 316px; vertical-align: baseline; perspective-origin: 332px 316px; "><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; perspective-origin: 309px 42px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><a target='_blank' href = "https://www.setgame.com/sites/default/files/instructions/SET%20INSTRUCTIONS%20-%20ENGLISH.pdf"><span style=""><span style="">SET</span></span></a><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style=""> is a card game in which players try to find valid 3-card sets from 12 cards on the table. What makes a valid set? Every card has four features, each with three possible values. In a valid set, each of the features, when looked at individually, are either the</span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style=""> </span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="font-style: italic; ">same</span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style=""> on each card OR</span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style=""> </span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="font-style: italic; ">different</span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style=""> on each card.</span></span></div><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 63px; white-space: pre-wrap; perspective-origin: 309px 63px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="">In this problem, you are given a 12x4 matrix representing 12 cards (rows) with 4 features (columns) each. The</span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style=""> </span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="font-style: italic; ">N</span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="">-th row corresponds to the</span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style=""> </span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="font-style: italic; ">N</span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="">-th card. Each feature has a value of 0, 1, or 2. Create a function that returns an Mx3 matrix of all valid sets, where each row is a set and each column is the index to a card in the set. For every set, the cards (columns) should be arranged in ascending order. If there are no valid sets for a given input, return []. You may assume that all cards are unique.</span></span></div><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="font-weight: bold; ">Example</span></span></div><div style="background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 120px; perspective-origin: 329px 120px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">cards = [1 0 1 0</span></span></div><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">         1 1 1 1</span></span></div><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">         2 2 1 0</span></span></div><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">         0 1 2 2</span></span></div><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">         2 1 1 1</span></span></div><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">         1 0 1 2</span></span></div><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">         0 0 0 0</span></span></div><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">         2 2 2 2</span></span></div><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">         0 2 0 0</span></span></div><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">         1 1 1 0</span></span></div><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">         0 1 0 2</span></span></div><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">         0 2 0 2];</span></span></div></div><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="">returns</span></span></div><div style="background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 20px; perspective-origin: 329px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">sets = [2 7 8</span></span></div><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; "><span style="border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; "><span style="margin-right: 0px; ">        6 8 11]</span></span></div></div><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="">because there are two valid sets. Cards 2,7, and 8 make one set and cards 6,8, and 11 form another set. Notice that a card can be a part of more than one set.</span></span></div></div></div>

<http://www.setgame.com/set/index.html SET> is a card game in which players try to find valid 3-card sets from 12 cards on the table. What makes a valid set? Every card has four features, each with three possible values. In a valid set, each of the features, when looked at individually, are either the _same_ on each card OR _different_ on each card.

In this problem, you are given a 12x4 matrix representing 12 cards (rows) with 4 features (columns) each. The _N_-th row corresponds to the _N_-th card. Each feature has a value of 0, 1, or 2. Create a function that returns an Mx3 matrix of all valid sets, where each row is a set and each column is the index to a card in the set. For every set, the cards (columns) should be arranged in ascending order. If there are no valid sets for a given input, return []. You may assume that all cards are unique.

*Example*

cards = [1 0 1 0
           1 1 1 1
           2 2 1 0
           0 1 2 2
           2 1 1 1
           1 0 1 2
           0 0 0 0
           2 2 2 2
           0 2 0 0
           1 1 1 0
           0 1 0 2
           0 2 0 2];

returns

sets = [2 7 8
          6 8 11]

because there are two valid sets. Cards 2,7, and 8 make one set and cards 6,8, and 11 form another set. Notice that a card can be a part of more than one set.

Solve

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Last Solution submitted on Nov 11, 2022

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Amro on 10 Aug 2012

A related question on Stack Overflow:

Asif Newaz on 15 Feb 2020

i dont understand it properly..how 6,8,11 is a valid set ?

Highphi on 26 Jul 2020

NOTE: That link has moved. It is now HERE: https://www.setgame.com/sites/default/files/instructions/SET%20INSTRUCTIONS%20-%20ENGLISH.pdf

Highphi on 26 Jul 2020

Also, I think you make a 'set' by combining 3 different cards so that, when combined, have 0 1 and 2 in each column or one of those options across entire column

for 2 7 8:
1 1 1 1
0 0 0 0
2 2 2 2
-- has 0, 1, 2 in each column

for 6 8 11,
1 0 1 2
2 2 2 2
0 1 0 2
-- has 0, 1, 2 in first three column and all 2s in last column

goc3 on 29 Sep 2020

Thank you, @Highphi. The link to instructions has been updated.

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Problem 840. SET (the card game)

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