Unformatted text preview: identiﬁed with a heap size, and the leftmost slot is numbered 0. So a game with a single coin is singleheap nim, and if there are two coins on the same slot, this means that the corresponding nim game has two heaps of the same size, etc. If a coin moves to the leftmost slot, that is equivalent to reducing that heap to 0. Now Bouton’s solution can be applied to Nimble, and the starting Ppositions are those in which the nimsum of the initial coin positions is 0. 1...
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 Spring '09
 MURALISTOYANOV
 Combinatorial game theory, Nim, bouton, Nimber, leftmost slot, corresponding nim game

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