Adriano Verdério, Izabele D'Agostin, Mari Sano, Patrícia Massae Kitani
{"title":"Algumas luminescências sobre o jogo Lights Out","authors":"Adriano Verdério, Izabele D'Agostin, Mari Sano, Patrícia Massae Kitani","doi":"arxiv-2403.17967","DOIUrl":null,"url":null,"abstract":"The theory behind the Lights Out game has been developed by several authors.\nThe aim of this work is to present some results related to this game using\nLinear Algebra. We establish a criterion for the solubility of this game in the\ncase of an $m$ by $n$ grid, which depends on the invertibility of a matrix, and\nwe present the conditions for this to occur, easily verifiable from $m$ and\n$n$. Furthermore, we explicitly determine the value of the determinant for a\nparticular case.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - History and Overview","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.17967","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The theory behind the Lights Out game has been developed by several authors.
The aim of this work is to present some results related to this game using
Linear Algebra. We establish a criterion for the solubility of this game in the
case of an $m$ by $n$ grid, which depends on the invertibility of a matrix, and
we present the conditions for this to occur, easily verifiable from $m$ and
$n$. Furthermore, we explicitly determine the value of the determinant for a
particular case.
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