A barber in a town has a sign on his door that says "I shave all the men in the town who do not shave themselves."
Does he shave himself?
If he does not shave himself, then he is a man who shaves himself, which goes against the rule that he only shaves those who do not shave themselves. But if he does shave himself, then he is a man who does shave himself, and therefore should not be shaved.
Solutions to this Paradox