Problem

Source: 2023 Tuymaada Junior P4

Tags: combinatorics, Game Theory, combinatorial game theory, Tuymaada



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