The Paradox of the Barber-brain teaser

Riddle 
In a town, there is a barber who shaves everyone who does not shave themselves, but he does not shave those who do shave themselves. Does the barber shave himself?

    This is a paradox. If the barber shaves himself, then he must not shave himself (because he shaves only those who don’t shave themselves). If he does not shave himself, then he must shave himself (because he shaves everyone who doesn’t shave themselves). The situation is logically impossible.