Consider the following game: a pile of n stones is placed in front of two players. The players
take turns removing 1, 2 or 3 stones from the pile. The player who removes the last stone
loses the game. Prove that if n gives a remainder of 1 when divided by 4 then the second
player has a winning strategy, i.e. can always win the game no matter how the first player
plays. Also prove that in all other cases the first player has a winning strategy.