Problem #PRU-100408

Problems Set theory and logic Algorithm Theory Game Theory Winning and loosing positions

Problem

Two clowns A and B are playing the following game. They have 33 tomatoes on a plate. One of the tomatoes is rotten and both clowns know which one. Each move they can choose one, two, or three of the remaining tomatoes from the plate and smash them into their own faces. They take turns and the clown who chooses the rotten tomato looses the game. They cannot skip the moves. Clown A starts the game. Does A or B have a winning strategy? (A winning strategy is a strategy following which you win no matter how your opponent plays.)