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Game involving stones on piles

Source: 2023 Tuymaada Junior P4

July 12, 2023
combinatoricsGame Theorycombinatorial game theoryTuymaada

Problem Statement

Two players play a game. They have n>2n > 2 piles containing n10+1n^{10}+1 stones each. A move consists of removing all the piles but one and dividing the remaining pile into nn nonempty piles. The player that cannot move loses. Who has a winning strategy, the player that moves first or his adversary?
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