Maximum Nim and Josephus Problem

In this study, we study the relation between Grundy numbers of a Maximum Nim and Josephus problem. Let f(x) = floor(x/k), where floor( ) is the floor function and k is a positive integer. We prove that there is a simple relation with a Maximum Nim with the rule function f and the Josephus problem in...

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Bibliographic Details
Published inarXiv.org
Main Authors Takahashi, Shoei, Manabe, Hikaru, Miyadera, Ryohei
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.03.2024
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Summary:In this study, we study the relation between Grundy numbers of a Maximum Nim and Josephus problem. Let f(x) = floor(x/k), where floor( ) is the floor function and k is a positive integer. We prove that there is a simple relation with a Maximum Nim with the rule function f and the Josephus problem in which every k-th numbers are to be removed.
ISSN:2331-8422