I invent a small board game, usually a reduced version of chess, and they have to implement both the rules and the AI. They use minimax, alpha-beta pruning, and then whatever optimizations they have time to throw in, such as bitboards, transposition tables, multithreading, and other methods. Then at the end of the 4 weeks we have a tournament between all the programs. It's quite fun and challenging. This year will be the 12th annual! I'm thinking of assigning a reduced version of refusal chess.