My fiance is taking a course in discrete structures and mathmatics. I found this question in her book and thought it was a good one.

<question>
A barber shaves all of those and only those people from his home town that don't shave themselves. Does the barber shave himself?
</question>

 

 

y

 

 

What if the barber if a female ?

 

 

The barber is a nomad and does not have a home town

 

 

I remembered this problem ! from C.L Liu ?

 

 

That reminds me of a test a teacher gave me in high school. I can't remember the questions (it was world history) but the effect was something like this:

1. 2 + 2 = 5
2. 6 / 2 = 4
3. 2 * 2 = 3
4. The answer to all of these questions is false.

 

 

no

 

 

I think the answer is vacuously true. Much like the statment, "all talking dogs have purple spots."

 

 

He cannot . He only shaves those who do not shave themself

But he must then shave himself as he shaves all people who do not shave themself

 

 

The barber is a man.

 

 

The barber can't exist

 

 

That's another good one...

 

 

the barber is 13... he doesn't have facial hair.

 

 

there is a lot of text out there about this dilema.

One of them:

http://home.att.net/~numericana/answer/sets.htm#barber

 

 

A barber shaves all of those and only those people from his home town that don't shave themselves. Does the barber shave himself?

Yeah, the barber shaves himself. Before the first time that the barber did the mass shaving, he was a "person that did not shave himself". That qualified him as a candidate for shaving. After the shaving was complete, he attained the status of a "person that shaved himself".

Of course, the barber may have shaved himself in the past, which, you may think, means that he is a "person that shaves himself" (you will see, later, that that is, in fact, false). Additionally, after the barber shaved himself and the rest of the unshaven in his town, his status of a "person that shaved himself" did not qualify him for any following mass shavings.

So now, the question becomes, are "people that no longer shave themselves" included in "people that don't shave themselves"?

If they are, then the answer most definitely could be that the barber shaved himself. After he shaves himself once, he no longer shaves himself until the next time he shaves himself. Which means that, after he shaves himself, he quickly falls back into the category of "people that don't shave themselves" and can once again, shave himself and the rest of the unshaven.

This begs the question, "well, since the other people in the town haven't shaved since the last time they shaved, does that mean that all people no longer shave themselves"? I think that is more of a matter of the person giving up on shaving. So, another assumption we must make about the barber is that after he shaves, he does not plan on shaving again. Rather, he gives up shaving forever and becomes a "person that no longer shaves themselves" and thus a "person that does not shave themselves".

When he starts his mass shaving project, and he falls under the category of a "person that does not shave themselves", he must shave himself whether he wants shaved or not.

So, in general: As long as the barber never plans to shave, he will shave himself.

Jason