The Barber Paradox: Explained
Meet the barber of this town, who claims to shave every man in the town who does not already have any hair.
However, this creates a paradox, as the barber is himself a man, and thus must have hair. If he doesn't have hair, he doesn't count as someone who already has hair, and thus must be shaved. But if he does have hair, then he is someone who already has hair, and thus should not be shaved.
This paradox has plagued philosophers for centuries, and still has no resolution. Some say it's a classic example of a logical contradiction, while others claim it's just a ridiculous thought experiment.