Circular Nim games (Q1953504)

Summary: 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.