{"title":"尼姆的游戏","authors":"L. Recht","doi":"10.2307/2303668","DOIUrl":null,"url":null,"abstract":"This is the binary representation of xi. By Bouton's above-mentioned condition, the numbers xi constitute a \"losing combination\" if and only if all the sums En= i bim are even. Since the bim are identical with the bi k, all the suns E= 1 bim are even if and only if all the sums 1 biik are even. By Bouton's condition again all the sums J=, bijk are even if and only if each of the sets of numbers aii, where j is fixed, constitutes a \"losing combination.\" From which the conclusion follows: The numbers xi constitute a \"losing combination\" if and only if each of the sets aii, where j is fixed, constitutes a \"losing combination.\" * C. L. Bouton, Annals of Math., ser. II, vol. 3, 1901, p. 35.","PeriodicalId":435813,"journal":{"name":"A Course in Game Theory","volume":"65 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1943-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Game of Nim\",\"authors\":\"L. Recht\",\"doi\":\"10.2307/2303668\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This is the binary representation of xi. By Bouton's above-mentioned condition, the numbers xi constitute a \\\"losing combination\\\" if and only if all the sums En= i bim are even. Since the bim are identical with the bi k, all the suns E= 1 bim are even if and only if all the sums 1 biik are even. By Bouton's condition again all the sums J=, bijk are even if and only if each of the sets of numbers aii, where j is fixed, constitutes a \\\"losing combination.\\\" From which the conclusion follows: The numbers xi constitute a \\\"losing combination\\\" if and only if each of the sets aii, where j is fixed, constitutes a \\\"losing combination.\\\" * C. L. Bouton, Annals of Math., ser. II, vol. 3, 1901, p. 35.\",\"PeriodicalId\":435813,\"journal\":{\"name\":\"A Course in Game Theory\",\"volume\":\"65 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1943-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"A Course in Game Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2307/2303668\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"A Course in Game Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2307/2303668","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
这是xi的二进制表示。根据鲍顿的上述条件，当且仅当所有的和En= i为偶数时，数字xi构成一个“输的组合”。因为b和k是相同的，所以当且仅当所有的和都是偶数时E= 1是偶数。根据Bouton的条件，所有的和J=， bijk都是偶数当且仅当每个集合aii，其中J是固定的，构成一个“损失组合”。由此得出结论:数字xi构成一个“失败的组合”当且仅当每个集合aii(其中j是固定的)构成一个“失败的组合”。C. L. Bouton，《数学年鉴》。,爵士。(二)1901年第三卷，第35页。
This is the binary representation of xi. By Bouton's above-mentioned condition, the numbers xi constitute a "losing combination" if and only if all the sums En= i bim are even. Since the bim are identical with the bi k, all the suns E= 1 bim are even if and only if all the sums 1 biik are even. By Bouton's condition again all the sums J=, bijk are even if and only if each of the sets of numbers aii, where j is fixed, constitutes a "losing combination." From which the conclusion follows: The numbers xi constitute a "losing combination" if and only if each of the sets aii, where j is fixed, constitutes a "losing combination." * C. L. Bouton, Annals of Math., ser. II, vol. 3, 1901, p. 35.
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