This one is from Bertrand Russell.
The Barber Paradox
A certain village has a barber named Saul. Saul is an affable fellow and is liked by everyone who knows him. But Saul has a peculiar practice from which he never waivers. He shaves all and only those adult male villagers who do not shave themselves. Now Saul is an adult male who lives in the village and he is clean-shaven. So an interesting question arises: Does he or does he not shave himself?
You might think that Saul does shave himself but this would contradict his practice of only shaving those individuals that do not shave themselves. Alternatively, you might think that Saul does not shave himself but this would contradict his practice of shaving all those individuals that do not shave themselves. Something has to give!?
* I should mention that Saul is a "normal" adult male and would have a beard if it were not for the fact that his face is regularly shaved.
(No cheating now... try to solve it on your own.)