@techreport{oai:ipsj.ixsq.nii.ac.jp:00234588, author = {Shoei, Takahashi and Yuki, Tokuni and Akito, Tsujii and Hikaru, Manabe and Ryohei, Miyadera and Shoei, Takahashi and Yuki, Tokuni and Akito, Tsujii and Hikaru, Manabe and Ryohei, Miyadera}, issue = {10}, month = {Jun}, note = {This study examines the relation between the Grundy numbers of a Maximum Nim and Josephus problem. Let f(x)=[x/k] where [ ] is a floor function and k is a positive integer such that k ≧ 2. We prove that there is a simple relation between a Maximum Nim with the rule function f and the Josephus problem, in which every k-th number is to be removed. Based on this relation, we propose a new method for solving the Josephus problem., This study examines the relation between the Grundy numbers of a Maximum Nim and Josephus problem. Let f(x)=[x/k] where [ ] is a floor function and k is a positive integer such that k ≧ 2. We prove that there is a simple relation between a Maximum Nim with the rule function f and the Josephus problem, in which every k-th number is to be removed. Based on this relation, we propose a new method for solving the Josephus problem.}, title = {Maximum Nim and Josephus Problem}, year = {2024} }