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Advances in Applied Mathematics
Perhaps the most famous combinatorial game is Nim, which was completely analyzed by C.L. Bouton in 1902. From then on, the variant of Nim game is getting more and more popular. This paper introduces a new variant of Nim game, K-L-Nim game, one player's illegal move is to remove k stones from one pile, while the other player's illegal move is to remove l stones from one pile. This paper gives a complete solution for the game by using Sprague-Grundy Theorem, Bouton Theorem and mathematicaldoi:10.12677/aam.2017.63027 fatcat:o2ldaarvqbaf7i7uaanjv2ebhi