Circular Nim Games
Matthieu Dufour, Silvia Heubach

TL;DR
This paper studies the structure of losing positions in Circular Nim, a two-player game involving token stacks arranged in a circle, providing initial results and open questions for future research.
Contribution
It characterizes losing positions for small n and k in Circular Nim and introduces open problems for further exploration.
Findings
Identified structure of losing positions for small n and k
Proposed open questions for larger n and k
Analyzed the game's combinatorial properties
Abstract
A circular Nim game is a two player impartial combinatorial game consisting of n stacks of tokens placed in a circle. A move consists of choosing k consecutive stacks, and taking at least one token from one or more of the k stacks. The last player able to make a move wins. We prove results on the structure of the losing positions for small n and k and pose some open questions for further investigations.
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Taxonomy
TopicsAuthorship Attribution and Profiling · Geometric and Algebraic Topology · Game Theory and Applications
