Barber's Paradox

In a small town, there is only one barbershop. Not all men in town go to the barber shop. Thus, the city's male population can be divided into two groups: those who shave alone and those who go to the barber.

So we assume the barber shaves all men who don't shave themselves, right? But does the barber shave or not shave his own? If not, he (as a "consumer") must shave his own, meaning he shaves his beard! But if he shaves himself, his person (as a consumer) joins the non-shaving group (so they go to the barber). So if he shaves himself, he doesn't shave himself!