Maximum Nim and Josephus Problem
Combinatorics
2024-03-29 v1
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.
Cite
@article{arxiv.2403.19308,
title = {Maximum Nim and Josephus Problem},
author = {Shoei Takahashi and Hikaru Manabe and Ryohei Miyadera},
journal= {arXiv preprint arXiv:2403.19308},
year = {2024}
}
Comments
This is the first result that treats the relation between general Josephus problem and the maximum nim