# One of the Toughest Riddles Ever?

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Yahoo News yesterday had a report on what is considered one of the “toughest riddles ever,” a classic paradox involving a barber that may thrill you or drive you bonkers. This is a variation of Russel’s paradox, and there are several ways to solve, or attempts to solve, this depending on how it is interpreted. The riddle is as follows:

There is a village where the barber shaves all those and only those who do not shave themselves. Who shaves the barber?

{Matzav.com Newscenter}

1. Why cant the barber be shaved by someone who does shave themselves?

Just because the BARBER shaves those that dont shave themselves doesnt mean that barber cannot be shaved by someone who does.

The restriction is on the barber. Yes, it is true that no one that does not shave themselves is shaved by another person (besides the barber). Given the option of the barber, all those that dont shave themselves are shaved by the barber. I dont see a restriction that those who shave themselves cannot shave others… it doesnt happen for the others only because of the availability of the barber. But if the barber was shaved by someone else who does shave themselves then the restriction doesnt apply.

The barber is in his own set. There are three… those that shave themselves, those that are shaved by the barber, and those that are shaved by those who shave themselves. The barber is the only one in the last set.

I think the confusion is a play on semantics to create logical premises falsely.

2. It can not be answered logically. It does not permit a self-referential set.

If the barber shaves himself, then he does not shave only those who do not shave themselves. If he doesn’t shave himself, he belongs to the set of people who do not shave themselves, resulting in a self-referential set. It becomes a case of the barber neither belonging inside the set nor outside it; although this statement seems contradictory, logically it is the only result which does not violate the premises presented in the paradox.

It is also akin to the philosophical question: “Who watches the Watchers?”

you also have to consider the inflection on the sentence: “He only shaves those who do not shave themselves.”

It can mean either those who do not perform self-shaving, OR it can mean those who do not shave, where shave is an action that can be performed either on oneself or on another (the barber shaves other people, and surely the act of shaving others isn’t limited only to the barber!).

So that sentence then, takes on two meanings:

1. He only shaves those who do not perform the act of shaving on themselves.

2. He only shaves those who do not perform the act of shaving on any person.

Following these premises, we can once again attempt to place the barber definitively in or out of the set of ‘people who do not shave themselves,’ and once again find that, according to interpretation #2, because he performs the act of shaving on others, he is unable to shave himself because he would then shave someone who does perform the act of shaving, in contradiction to the previous statement that he does not do so.

3. it is very tricky. First two definitions:

def 1) All and only those who shave themselves = S

def 2) All people in the village, including the barber, are either members of S or members of not-S. there is no one in the village that is a member of both.

If the barber shaved himself then he would be a member of S.
If the barber does not shave himself then he would be a member of not-S.

A barber who must shave all and only not-S can not shave any S

The barber can not shave himself, because he would be shaving a member of S

if the barber is not a self shaver then he is a member of not-S

The barber must shave himself because he must shave all members of not-S

Thus he must both shave and not shave himself

No one else in the village can shave the barber because only the barber can shave members of not-S.

4. Why is that a paradox?

Some people shave themselves, the barber does not. Of those that dont shave themselves, the barber shaves them. All this means is that no one, other than the barber, shaves anyone else that the barber doesnt shave.

This means that anyone and everyone can shave the barber besides the barber himself.

The fact that some one other person can shave the barber does not contradict any of these premises. Because what appears to be a logical biconditional is actually resolved by understanding basic grammar… subject and object. The barber is the individual that the premise applies to, no one else. There are no restrictions on anyone else besides one, that no one shaves someone else besides the barber. No one that is shaved by someone else is shaved by someone not the barber – except for the barber.

5. The answer is a paradox too. The answer is that he(the unshaven barber) doesn’t shave himself-ever!, So, he(the village barber) is going to have to do it for him. Split personality disorder?

6. Not quite a paradox. It’s a logical strange loop. Like saying “Yankel always lies” then having Yakel say “I lied” The original statement sounds fine until self – refrentiality is applied to the barber.

7. Well: if you can’t find a place for the barber, then, obviously, the first statement has to be wrong.

8. no one shaves the barber who said he shaves? and the barber doesnt shave anyone because they themselves dont shave

9. a man is sentenced to death. the elders tell him that he has one wish. if they fulfill it, his death will be by fire. if they do not fulfill his wish, he will get off easier and they will hang him which is the easier of the two. what should he wish for?

10. the barber is frum and his customers are goyim. he has a beard and there is no problem shaving goyim. on the other hand, he cannot permit a goy to shave him because of sakanah, ergo…

11. Someone from outside the village shaves the barber. Or the barber himself lives outside the village so the rule doesn’t apply to him and he can shave himself outside that village.

12. I believe the answer has something to do with this:

Only men need to be shaved

Who says the barber is male? The barber doesn’t need to be shaved. Why are you presupposing that the barber is a male?

13. “Think out of the box” is right.

The barber is a woman.

This is one of the oldest logic paradoxes around. The moss has been growing on it for at least a century. (I think our AP math class suffered through it in ninth grade.)

14. If there is a person in the village who is shaved by himself and shaved by the barber, then the declaration “all of those and only those who do not shave themselves are shaved by the barber” is obviously wrong.

The other possibility would be that the barber is a woman or has no beard growth and therefore has no need to shave.

15. he shaved with shaving cream so the shaver must shave the shaveee unless he was sitting shiva or in 9 days unless he has an illness or a shidduch date and therefore a heter but its very sophisticated and must be thiught out out

16. a) woman barber – no shaving necessary.
b) barber shaves all villagers, and THEN shaves himself. While being the barber, he hasn’t shaved himself, after shaving himself he is no longer the barber.

(albeit these are major cop-outs…)

17. I find that todays Daf Yomi on Daf 87 provides a far better riddle than this one. I refer to the story of the boy who has a flask and a pundyon (A coin) who goes to buy something for his father. Well worth reading.

18. (For anyone who reads this later on, Daf Yomi is referring to Bava Basra)

So the barber is a woman? Meh, I still like the Torah answers best ðŸ™‚

19. The reason why it is a paradox is because it says that the barber shaves AA those who don’t shave themsemselves. So if he were to be shaved by someone else in the village (as some suggested), he would not be shaved by himself, so he would have to shave himself. so he does shave himself, so he cannot shave himself etc.

20. The answer is obviously a paradox. If the barber (even if she is a woman) doesn’t shave himself, then he has to because he shaves everyone who doesn’t shave his or herself. To those who say the barber isn’t shaved at all (because the barber is either a woman or has a beard) that is a contradictory statement. If he isn’t shaved, then he obviuosly doesn’t shave himself, right? But, if he doesn’t shave himself then he does because he shaves anyone who doesn’t shave his ore herself!

21. I think the barber shaves his beard himself. This is because the barber shaves only those people who do not shave themselves. This means either the people do not know to shave or do not want to shave themselves . If people do not know to shave themselves how would they shave the barber.if the people are too lazy to shave their beard themselves how would they shave someone else beard??? The barber shaves only those who don’t shave themselves. But the barber is not one of the people who do not shave because the barber knows to shave and he is not lazy to shave so if the barber can shave others then he can shave himself too.