| for all n ≥ 1. Two conjectures were proposed on the game by Fraenkel [7]. (2008) | |||||||||||||||||
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| Abstract. The N-heap Wythoff’s game is a two-player impartial game with N piles of tokens of sizes A1,..., AN, A1 ≤ · · · ≤ AN. Players take turns removing any number of tokens from a single pile, or removing (a1,..., aN) from all piles — ai tokens from the i-th pile, providing that 0 ≤ ai ≤ Ai, �N i=1 ai> 0 and a1 ⊕ · · · ⊕ aN = 0, where ⊕ is the nim addition. The first player that cannot make a move loses. Denote all the P-positions (i.e., losing positions) by (A 1,..., A N−2, A N−1 n | |||||||||||||||||
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