Let's work our brains a bit

Betrand Russell came up with this paradox (in my own words):

In a town, a barber shaves all and only those who don't shave themselves.

Is there anything wrong with this scenario? Sounds rather normal actually, doesn't it? Well, let us ask, however, if the barber shaves himself. Suppose that he does. It certainly makes sense to say the barber shaves himself, since he saves money that way without having to go to another barber.

But, wait a minute. So the barber shaves himself? Yet it is said that the barber shaves all and only those who don't shave themselves! If the barber shaves himself, he doesn't qualify under the set of people who don't shave themselves. So the barber can't shave himself!

Alright, not a problem. We'll just restrain the barber from shaving himself, on pains of committing a paradox. So the barber doesn't shave himself.

But wait again! Did you just say that the barber doesn't shave himself? Well then, he qualifies now under the set of people who don't shave themselves! And according to what is stated, he has to shave himself, since he shaves all and only those people who don't shave themselves, which includes himself!

But if he shaves himself, then he cannot shave himself.

If he cannot shave himself, then he has to shave himself.

A paradox! So does the damn barber shaves himself or not?!
Well, simple. This barber doesn't exist. He is a walking paradox. There is no trick in this analysis, other than being vague to leave out the technicalities. Some food for thought huh?