Slow k-Nim
نویسندگان
چکیده
Given n piles of tokens and a positive integer k ≤ n, we study the following two impartial combinatorial games Nimn,≤k and Nim 1 n,=k. In the first (resp. second) game, a player, by one move, chooses at least 1 and at most (resp. exactly) k non-empty piles and removes one token from each of these piles. For the normal and misère version of each game we compute the Sprague-Grundy function for the cases n = k = 2 and n = k + 1 = 3. For game Nimn,≤k we also characterize its P-positions for the cases n ≤ k + 2 and n = k + 3 ≤ 6.
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