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Article

More about Exact Slow k-Nim

Chikin N., Gurvich V., Knop K., Paterson M., Vyalyi M.

Given n piles of tokens and a positive integer k \leq n, the game Nim^1_{n,=k} of exact slow k-Nim is played as follows. Two players move alternately. In each move, a player chooses exactly k non-empty piles and removes one token from each of them. A player whose turn it is to move but has no move loses (if the normal version of
the game is played, and wins if it is the misere version). In Integers 20 (2020), #G3, Gurvich et al. gave an explicit formula for the Sprague-Grundy function of Nim^1_{4,=2}, for both its normal and misere versions. Here we extend this result and obtain an explicit formula for the P-positions of the normal version of Nim^1_{5;=2} and Nim^1_{6,=2}.