Combinatorial Games

Two children take turns breaking up a 6 square by 8 square rectangular chocolate bar. They break the bar only at the divisions between the squares. If the bar breaks into several pieces, they keep breaking one piece at a time until only the squares remain. The first player who cannot make a break is the loser. Who will win? This course focuses on games like this one, called combinatorial games. Their names are nim, hackenbush, Grundy's game, kayles, and cram. Each student will become a specialist in one or more games, and will write a paper about how this game can be perfectly played. Knowledge of binary arithmetic is essential. Algebra II is a prerequisite.