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      Maximum Nim and Josephus Problem

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          Abstract

          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.

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          Author and article information

          Journal
          28 March 2024
          Article
          2403.19308
          1e345603-be52-48da-91e1-5e3459ed0e2e

          http://creativecommons.org/licenses/by/4.0/

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          Custom metadata
          91A46, 91A05
          This is the first result that treats the relation between general Josephus problem and the maximum nim
          math.CO

          Combinatorics
          Combinatorics

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