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The (in)famous Barber (Posted on 2002-05-14) Difficulty: 3 of 5
In a certain small town, there is a barber named Bill. Since Bill is the only barber in the town, he decides that he will shave all the town's residents who do not shave themselves, but (obviously) not the ones who do.

If Bill follows this rule, will he shave himself or not?

See The Solution Submitted by levik    
Rating: 3.4500 (20 votes)

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Solution NOT a paradox! IMPORTANT distinction! | Comment 20 of 35 |
It's not actually a paradox, it's a contradiction (as humpty dumpty tells Alice eloquently in... through the looking glass?).

If I were to say, here's a great paradox: I met a man who was 4 foot tall AND 6 foot tall, what do you think of that?!?

It's perfectly obvious that that wouldn't be a paradox, because there simply couldn't be such a man. Likewise, such a barber could never exist. This isn't a meanigless statement, the distinction between paradoxes and contradictions is very important. After all, it's certainly true that I can utter the statement "This statement is a lie," and so we then have to puzzle around at the boundaries of logic to work out what's wrong.

In this case, however, the puzzle is saying "In a certain town there is a barber that neither shaves himself nor does not shave himself, which is akin to saying "In a certain town there is a man who is six foot tall and four foot tall."

Not that it's a bad puzzle though... :)
  Posted by sam on 2003-09-06 16:02:21
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