MathDB
2, 4, 5-Nim

Source: Philippines MO 2016/4

January 21, 2017
combinatoricsgamenim

Problem Statement

Two players, AA (first player) and BB, take alternate turns in playing a game using 2016 chips as follows: the player whose turn it is, must remove ss chips from the remaining pile of chips, where s∈{2,4,5}s \in \{ 2,4,5 \}. No one can skip a turn. The player who at some point is unable to make a move (cannot remove chips from the pile) loses the game. Who among the two players can force a win on this game?