Barber Paradox

Paradox
There exists a community, one of whose members is a barber.

This barber operated under an unusual rule: his task was to shave every man in the community who did not shave himself.

Who shaves the barber?

If he does not shave himself, then he must shave himself.

But if he shaves himself, he must not shave himself.

Resolution
This is an application of Russell's Paradox.

History
Bertrand Russell himself used it as an illustration of his paradox, claiming it was invented by an unnamed acquaintance of his.