{"title":"The 5-Way Scale","authors":"T. Khovanova, Joshua Lee","doi":"10.2478/rmm-2019-0001","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we discuss coin-weighing problems that use a 5-way scale which has five different possible outcomes: MUCH LESS, LESS, EQUAL, MORE, and MUCH MORE. The 5-way scale provides more information than the regular 3-way scale. We study the problem of finding two fake coins from a pile of identically looking coins in a minimal number of weighings using a 5-way scale. We discuss similarities and differences between the 5-way and 3-way scale. We introduce a strategy for a 5-way scale that can find both counterfeit coins among 2k coins in k + 1 weighings, which is better than any strategy for a 3-way scale.","PeriodicalId":120489,"journal":{"name":"Recreational Mathematics Magazine","volume":"326 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Recreational Mathematics Magazine","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/rmm-2019-0001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Abstract In this paper, we discuss coin-weighing problems that use a 5-way scale which has five different possible outcomes: MUCH LESS, LESS, EQUAL, MORE, and MUCH MORE. The 5-way scale provides more information than the regular 3-way scale. We study the problem of finding two fake coins from a pile of identically looking coins in a minimal number of weighings using a 5-way scale. We discuss similarities and differences between the 5-way and 3-way scale. We introduce a strategy for a 5-way scale that can find both counterfeit coins among 2k coins in k + 1 weighings, which is better than any strategy for a 3-way scale.
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