Modular Nim, also known as Kotzig’s Nim, is an impartial, two-player combinatorial game invented by Anton Kotzig in 1946. The game is played using a token placed on a circular board of n spaces and a set M of possible moves. On his turn, a player selects a move from M and advances the token accordingly around the board to a previously unoccupied space. In normal play, the last player who is able to move wins the game. To date, much research into Modular Nim has focussed on determining the P-positions for various combinations of n and M. In this paper, we calculate the Sprague-Grundy values of certain instances of the game.
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