2, 4, 5-Nim
Source: Philippines MO 2016/4
January 21, 2017
combinatoricsgamenim
Problem Statement
Two players, (first player) and , take alternate turns in playing a game using 2016 chips as follows: the player whose turn it is, must remove chips from the remaining pile of chips, where . 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?