E. Chen, William Du, Tanmay Gupta, T. Khovanova, Alicia Li, Srikar Mallajosyula, Rohit Raghavan, Arkajyoti Sinha, Maya Smith, Matthew Qian, Samuel Wang
{"title":"魔术集正方形的分类","authors":"E. Chen, William Du, Tanmay Gupta, T. Khovanova, Alicia Li, Srikar Mallajosyula, Rohit Raghavan, Arkajyoti Sinha, Maya Smith, Matthew Qian, Samuel Wang","doi":"10.2478/rmm-2020-0005","DOIUrl":null,"url":null,"abstract":"A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations and reflections of the square. Under these transformations, there are 21 types of magic SET squares. We calculate the number of squares of each type. In addition, we discuss a game of SET tic-tac-toe.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"78 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Classification of Magic SET Squares\",\"authors\":\"E. Chen, William Du, Tanmay Gupta, T. Khovanova, Alicia Li, Srikar Mallajosyula, Rohit Raghavan, Arkajyoti Sinha, Maya Smith, Matthew Qian, Samuel Wang\",\"doi\":\"10.2478/rmm-2020-0005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations and reflections of the square. Under these transformations, there are 21 types of magic SET squares. We calculate the number of squares of each type. In addition, we discuss a game of SET tic-tac-toe.\",\"PeriodicalId\":429168,\"journal\":{\"name\":\"arXiv: History and Overview\",\"volume\":\"78 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: History and Overview\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/rmm-2020-0005\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: History and Overview","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/rmm-2020-0005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations and reflections of the square. Under these transformations, there are 21 types of magic SET squares. We calculate the number of squares of each type. In addition, we discuss a game of SET tic-tac-toe.
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