The barber paradox is a bit of mental gymnastic derived from Russel's paradox, that shows that an apparently plausible scenario is allegedly logically impossible:
Suppose there is a town with just one barber, who is male. In this town, every man keeps himself clean-shaven, and he does so by doing exactly one of two things:Starting from this, one is supposed to ask the question "Who shaves the barber?", which allegedly leads to the paradox...
- shaving himself; or
Also, "The barber is a man in town who shaves all those, and only those, men in town who do not shave themselves."
- being shaved by the barber.
In this day and age the solution ought to be simple though; the barber is logically a woman*. Simple as that!
*) At least in Norwegian that is - the term "a man" is often used (correctly or incorrectly) as a somewhat genter neutral way of saying "a person".