Use the verb outwit to describe using your brain to beat an opponent, like outwitting someone by figuring out the answer to a difficult riddle.
Wit comes from the Old English word witan, which means "to know." So someone who outwits another person knows more — or at least knows more than the person thought. You can outwit someone with clever words, or with craftiness on the playing field. An unexpected strategy can help one side outwit the other on the battlefield.