• (A partisan Subtraction game) Starting with a pile of x N chips, two players, I and II, alternate taking a certain number of chips. Player I can remove 1 or 4 chips. Player II can remove 2 or 3 chips. The last player who removes chips wins the game.
• Show that, from a starting position of 11 chips, the next player to play has a winning strategy.
• If the starting position has more than 11 chips, which player has a winning strategy? Describe the winning strategy.