# The barber paradox - Who shaves the barber? [closed]

All the men in a village either shave themselves or are shaved by a barber (himself a man from the village).

The barber claims to shave only the male villagers who do not shave themselves.

So who shaves the barber
?

Please explain in very simple ways .

• I vote to close this as too broad Commented Aug 26, 2016 at 19:57
• This is a well known mathematical paradox. There's plenty of material on this on the web, and I'm not sure if this is just looking for some trick answer. It's an application of Russell's paradox. Commented Aug 26, 2016 at 20:07
• At least say that you didn't create this yourself. Commented Aug 27, 2016 at 6:07
• I vote to close this as a copy/paste of a well known paradox. Commented Aug 27, 2016 at 6:18

A simple explanation of the underlying paradox is

that it is the same as asking "can there be a book in a library that lists all the books in the library that do not contain any lists?"
If the said book contains such a list it should not be listed while if it does not contain such a list it should - paradox.

Formerly, and slightly more strict, as will become apparent: "if R is the set of all sets that do not contain themselves does R contain itself or not?" (the Russell paradox).

A problem posed in the form of such a paradox can have a solution if

It is phrased like the informal example above. The book may be the only book in the library and contain some other list - it is then true, in a sense, that it lists all the books in the library that do not contain any lists.

But for the problem, as posed, this attack does not work.

A possible solution, albeit an admittedly weak one, to the problem, as posed, is

that the barber shaves himself or someone else shaves him or neither or both.

The barber is from the village. The barber has moved to a town, where he works as a barber. All the men in the village that the barber is from who do not shave themselves go to the town to be shaved by the barber.