The barber paradox is a puzzle derived from Russell's paradox. It was suggested to Bertrand Russell as an illustration of the paradox, but he deemed it an invalid modification of his paradox. The puzzle shows that an apparently plausible scenario is logically impossible. Specifically, it describes a barber who is defined such that he both shaves himself and does not shave himself, which implies that no such barber exists.
Paradox
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The barber is the "one who shaves all those, and those only, who do not shave themselves". The question is, does the barber shave himself?