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## #1 2006-06-01 09:03:46

AshJones555
Member
Registered: 2006-05-15
Posts: 19

A town has only one male barber. If he shaves every man in the town except for those who shave themselves, does he shave himself?

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## #2 2006-06-01 09:57:56

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

Maybe just one hair at a time:

Status: I don't shave myself
Action: "snip"
Status: I do shave myself
Action: (stops, waits, looks around, notices lack of self-shaving)
Status: I don't shave myself
Action: "snip"
...

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #3 2006-06-01 11:00:00

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

I cannot believe that I cannot believe that I am not the one who thought up this answer.

igloo myrtilles fourmis

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## #4 2006-06-01 17:01:22

RealEstateBroker
Member
Registered: 2006-06-01
Posts: 45

I figured out the answer. At first I wondered whether this was just one of those apparent paradoxes, resulting from a clever use of words; but when I realized what the solution is, I saw that there really is an answer. The solution has to do with an (incorrect) assumption that people will generally make upon hearing the question. When you are able to get past that assumption, then it becomes easy to figure out the correct answer. So, I am new here: Can someone tell me whether I am supposed to disclose the answer I came up with, or does that ruin it for everyone else?

Love is what matters most!

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## #5 2006-06-01 21:40:11

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

Hi Real! And welcome to the forum.

Yes, you can provide your solution - I am keen to read it!

If you want to, you can put the answer inside "hide" tags. They work like this:

And is done like this:

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #6 2006-06-01 23:35:51

Zach
Member
Registered: 2005-03-23
Posts: 2,075

Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.

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## #7 2006-06-02 20:16:16

justlookingforthemoment
Moderator
Registered: 2005-05-26
Posts: 2,161

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## #8 2006-06-03 06:31:11

RealEstateBroker
Member
Registered: 2006-06-01
Posts: 45

Love is what matters most!

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## #9 2006-06-03 06:39:14

RealEstateBroker
Member
Registered: 2006-06-01
Posts: 45

Zach wrote:

Love is what matters most!

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## #10 2006-06-03 06:41:31

RealEstateBroker
Member
Registered: 2006-06-01
Posts: 45

I just want to thank the Administrator for welcoming me to this forum, and for explaining how to hide the answer.

Love is what matters most!

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## #11 2006-06-03 11:50:28

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

And a very good answer ... well done!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #12 2006-06-03 18:29:08

ganesh
Registered: 2005-06-28
Posts: 24,300

RealEstateBroker has actually given an acceptable solution! Well done!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #13 2006-06-03 18:39:13

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

Wikipedia doesn't give the answer, though.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #14 2006-07-11 09:46:03

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

AshJones555 wrote:

A town has only one male barber. If he shaves every man in the town except for those who shave themselves, does he shave himself?

The problem implies the barber, being male, is shaven.

Another one:

This sentence is false.

True or False?

You can shear a sheep many times but skin him only once.

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## #15 2006-07-11 11:22:19

mikau
Member
Registered: 2005-08-22
Posts: 1,504

I think I've got a possible solution.

A logarithm is just a misspelled algorithm.

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## #16 2006-08-28 02:28:27

cronodragon
Member
Registered: 2006-08-27
Posts: 6

One question: what happens when a paradox like that is solved? I mean, that something that seems false, is indeed true and returns an answer?

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## #17 2007-07-31 21:05:43

fireprincess59
Member
Registered: 2007-07-31
Posts: 1

Unfortunately, Real, he would not be considered a boy if he were working. Also, the term 'man' can be implied to the population of the world as a whole, and as such, can be applied to the population to the town which is a much smaller scale as it doesn't even work that way if we imply that the baber is actually female. Unfortunately, not all of the paradox is there, for yes, it is a paradox, and a nicely woven one as well, for the wording is just magnificent. I actually just read up on said paradox, and I do know the actual answer. However, I have yet to figure out how this is related to math, for every site I've been to so far has given it as a math paradox, when no math is included. What should be up here is a 'heap' paradox, such as this.

Assume the following two statements are true:

1. If you have zero dollars, you are not rich.
2. If you add a dollar, then you are still not rich.

As neither statement states and ending to the cycle, or a point in which you will become rich, and the second statement doesn't state to how much money you are adding said dollar to, you could have an infinite amount of dollars and you would still not be rich.

Oh, yes, the answer. Well, here it is.

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## #18 2007-08-01 04:18:56

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Assume the following two statements are true:

1. If you have zero dollars, you are not rich.
2. If you add a dollar, then you are still not rich.

As neither statement states and ending to the cycle, or a point in which you will become rich, and the second statement doesn't state to how much money you are adding said dollar to, you could have an infinite amount of dollars and you would still not be rich.

This sort of paradox is typically phrased with a boat.  If you have a boat and you replace one of it's planks, it is still the same ship.  The same if you replace n+1.  But if you replace all of its planks, many would consider this a new ship.

The problem lies with using induction on something in which there is no clear cut transition, but that one certainly exists.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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