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Here's how Alice, who doesn't even know the rules to chess, can defeat a grandmaster. (This is sometimes called the Chess Grandmaster Problem.) She challenges both Gary Kasparov and Anatoly Karpov to a game, at the same time and place, but in separate rooms. She plays white against Kasparov and black against Karpov. Neither grandmaster knows about the other. Karpov, as white, makes his first move. Alice records the move and walks into the room with Kasparov. Playing white, she makes the same move against Kasparov. Kasparov makes his first move as black. Alice records the move, walks into the room with Karpov, and makes the same move. This continues, until she wins one game and loses the other, or both games end in a draw.