Circular Nim Games

  • Matthieu Dufour
  • Silvia Heubach
Keywords: Combinatorial Games, Nim, winning strategy


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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