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I was working my way through some puzzles , when I came across the following question:

  • An ancient Sicilian legend says that the barber in a remote town who can be reached only by traveling a dangerous mountain road

  • The barber shaves those people, and only those people, who do not shave themselves.

  • Can there be such a barber?

My solution:

If the barber is a Female - then YES such a barber exists
For the sake of simplicity , let us assume that the Barber is a Male and that all Males have a Fuzz / Facial Hair
Let us assume that such a Male Barber exists
If the barber shaves himself then he infringes the rule that he shaves only those who do not shave themselves
If the barber does not shave himself then the rules say that he must shave himself
This is a Paradox and hence no Male Barber Exists !

My question:

Am I correct ?

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    $\begingroup$ I remember a version of this paradox where the barber is explicitly assumed to be a man. Without that assumption, the whole story just says that the barber is a female and there is no paradox (if one assumes that women don't shave [!]). $\endgroup$ – GOTO 0 Jan 1 '15 at 5:36
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    $\begingroup$ Found it: Barber paradox $\endgroup$ – GOTO 0 Jan 1 '15 at 5:40
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    $\begingroup$ I don't see how you can assume that females don't shave. I mean, it doesn't even state what the barber shaves - it could be legs, for all we know. Logically, the answer is just a paradox with no solution, similar to "the set of all sets that do not contain themselves," or Russell's Paradox. $\endgroup$ – mdc32 Jan 1 '15 at 5:41
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    $\begingroup$ Well @mdc32 , a barber usually shaves the facial hair or head hair ;) $\endgroup$ – pranav Jan 1 '15 at 5:45
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    $\begingroup$ I would say yes. It is a rather interesting situation, but the wiki page is easy to find and in-depth, so I'm afraid we can't give much more information. $\endgroup$ – mdc32 Jan 1 '15 at 5:54
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No, you are wrong.

The barber is stated to shave "those people, and only those people, who do not shave themselves".

  • If we assume the barber is a person, they cannot exist.
  • If they did exist, and did not shave themselves, the must shave themselves, which forbids them from shaving themselves, etc...

It works if they're not a person.

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The barber doesn't shave.

Perhaps the barber is a woman or a child or perhaps he's a man with a great big bushy beard and moustache or maybe he's undergoing hormone treatment and doesn't need to shave - doesn't matter which.

If you want it to be a paradox then you need to add that all the men in the village are clean-shaven and that they are all shaved by someone from the village and that only men are allowed to be barbers (or that kind of thing). And that magic doesn't exist and there aren't any auto-shaving machines. Also no access to electrolysis or waxing or depilatory creams.

Also (if you want it to be a paradox) you might want to stipulate that the number of men is > 0 and the number of barbers is >= 1. And that the people are homo sapiens and that none of them is undergoing medical treatment which could cause hair loss, or has radiation poisoning.

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    $\begingroup$ are you serious @AE , ha ha ha :) $\endgroup$ – pranav Jan 3 '15 at 14:45
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    $\begingroup$ @pranav, not entirely serious. :) $\endgroup$ – A E Jan 3 '15 at 15:23
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    $\begingroup$ This is wrong. The barber is described as shaving all people who do not shave themselves. If there are people who are not being shaved at all then that is sufficient to conclude that such a barber does not exist. $\endgroup$ – Taemyr Jan 6 '15 at 10:01
  • $\begingroup$ @AE No, you misunderstand the other answer, it makes no such assumption. I will attempt to clarify by changing the formulation to not be logically impossible, "The barber shaves those people, who neither shave themselves or are occupied as barbers". Under this formulation, as in the OP, if a single person(non-barber in the new formulation) does not shave at all this barber can not exist - because he would not shave the person who does not shave. $\endgroup$ – Taemyr Jan 6 '15 at 11:43
  • $\begingroup$ @Taemyr, depends whether the barber shaves all of the people who don't shave themselves, or only some of them. The original question is silent on this point. It says that every person shaved by the barber is a person who does not shave themselves, but it doesn't say that every person who does not shave themselves is shaved by the barber. A baby, for example, neither shaves themselves nor is shaved by a barber - under normal circumstances. Perhaps if they were a werewolf and the parents were hiding it? $\endgroup$ – A E Jan 6 '15 at 11:53

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