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aboxofchocolates
Joined: 21 Mar 2008
Location: on your mind
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 Posted: Sun Nov 29, 2009 4:44 pm Post subject: |
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| beercanman wrote: |
There seems to be disagreement on the answer. On the China off-topic forum one guy says he uses the "pigeonhole principle" - if you have more pigeons than holes than at least one hole must have at least 2 birds. I figured since the question didn't say all dogs must have hair, then one dog can be bald. So the number of hairs can range from 0 to one less than the number of dogs, meaning two dogs need not have the same number of hairs, yet still fitting the question's needs. If all dogs must have at least one hair, then at least two will have the same number of hairs.
All cleared up? |
Ok, I thought it was either no dogs could have the same number of hairs or two dogs must have the same number of hairs.
http://www.learn4good.com/games/puzzle/boat.htm
Here you go! |
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tfunk
Joined: 12 Aug 2006
Location: Dublin, Ireland
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| Posted: Sun Nov 29, 2009 4:59 pm Post subject: |
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| beercanman wrote: |
There seems to be disagreement on the answer. On the China off-topic forum one guy says he uses the "pigeonhole principle" - if you have more pigeons than holes than at least one hole must have at least 2 birds. I figured since the question didn't say all dogs must have hair, then one dog can be bald. So the number of hairs can range from 0 to one less than the number of dogs, meaning two dogs need not have the same number of hairs, yet still fitting the question's needs. If all dogs must have at least one hair, then at least two will have the same number of hairs.
All cleared up? |
The pigeonhole principle is the same as what Fox was describing, but as you pointed out it is possible for the number of hairs to be 0. So, you cannot prove the conclusion either way from the data given, unless you assume that at least two will have the same number of hairs. |
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tfunk
Joined: 12 Aug 2006
Location: Dublin, Ireland
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| Posted: Sun Nov 29, 2009 5:11 pm Post subject: |
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Bravo!
I gotta admit I got it more out of random clicking about than anything else.  |
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beercanman
Joined: 16 May 2009
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| Posted: Sun Nov 29, 2009 5:51 pm Post subject: |
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| tfunk wrote: |
[
The pigeonhole principle is the same as what Fox was describing, but as you pointed out it is possible for the number of hairs to be 0. So, you cannot prove the conclusion either way from the data given, unless you assume that at least two will have the same number of hairs. |
The question does not exclude a bald dog. So you cannot prove two dogs have the same number of hairs. |
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Koveras
Joined: 09 Oct 2008
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| Posted: Sun Nov 29, 2009 8:07 pm Post subject: Re: A little logic problem |
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| It seems to me that if we accept the zero hair count, we can't even prove that there are two dogs - there might only be one. In that case, beercanman is still right, but for a different reason than the one he explained. |
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Fox
Joined: 04 Mar 2009
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| Posted: Sun Nov 29, 2009 8:24 pm Post subject: Re: A little logic problem |
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| Koveras wrote: |
| It seems to me that if we accept the zero hair count, we can't even prove that there are two dogs - there might only be one. In that case, beercanman is still right, but for a different reason than the one he explained. |
This is another good point. |
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Fox
Joined: 04 Mar 2009
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| Posted: Sun Nov 29, 2009 8:31 pm Post subject: |
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| aboxofchocolates wrote: |
| beercanman wrote: |
There seems to be disagreement on the answer. On the China off-topic forum one guy says he uses the "pigeonhole principle" - if you have more pigeons than holes than at least one hole must have at least 2 birds. I figured since the question didn't say all dogs must have hair, then one dog can be bald. So the number of hairs can range from 0 to one less than the number of dogs, meaning two dogs need not have the same number of hairs, yet still fitting the question's needs. If all dogs must have at least one hair, then at least two will have the same number of hairs.
All cleared up? |
Ok, I thought it was either no dogs could have the same number of hairs or two dogs must have the same number of hairs.
http://www.learn4good.com/games/puzzle/boat.htm
Here you go! |
Pretty fun, I like it better than the simpler chicken/fox/grain variant. |
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Koveras
Joined: 09 Oct 2008
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| Posted: Sun Nov 29, 2009 8:32 pm Post subject: Re: A little logic problem |
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| Fox wrote: |
| Koveras wrote: |
| It seems to me that if we accept the zero hair count, we can't even prove that there are two dogs - there might only be one. In that case, beercanman is still right, but for a different reason than the one he explained. |
This is another good point. |
I'm tempted to say that the zero hair count makes the question internally inconsistent, and for that reason shouldn't be allowed. Then again, one could also make the case that it's a trick question within a trick question. |
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daniel-andersson
Joined: 13 Jul 2009
Location: Seoul (but from Sweden)
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| Posted: Sun Nov 29, 2009 8:45 pm Post subject: Re: A little logic problem |
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| beercanman wrote: |
(stolen from China off-topic forum)
GIVEN: The number of dogs in the world is greater than the number of hairs on any one dog.
PROVE: That there are (or or not) two dogs with the same number of hairs. |
Since there are at least 0 hair on a dog, it mean that we at least have one dog. Lets say that we have K amount of dogs here, so K is equal or greater than 1.
In case there are no bald dogs here there exist at least a dog with more than 0 hairs. This assumption gives that there exist a dog with atleast one hair here which also mean that there at least exist two dogs here.
And since the Chinese Forum has the same problem as us its clear that China as well at least have one dog, so there exist C dogs in China. So C is equal or greater than 1.
K+C is equal or greater than 2. So its proved that we atleast have two dogs in the world.
In case there exist no bald dog here its clear that there are at least two dogs here with the same amount of hairs.
In case there exist no bald dog in China its clear that there are at least two dogs in China with the same amount of hairs.
In case there exist a bald dog in China and here there would be two dogs with no hairs in the world, hence the whole statement is proven without any assumptions.
Last edited by daniel-andersson on Sun Nov 29, 2009 9:12 pm; edited 1 time in total |
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Fox
Joined: 04 Mar 2009
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| Posted: Sun Nov 29, 2009 9:04 pm Post subject: Re: A little logic problem |
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| Koveras wrote: |
| Fox wrote: |
| Koveras wrote: |
| It seems to me that if we accept the zero hair count, we can't even prove that there are two dogs - there might only be one. In that case, beercanman is still right, but for a different reason than the one he explained. |
This is another good point. |
I'm tempted to say that the zero hair count makes the question internally inconsistent, and for that reason shouldn't be allowed. Then again, one could also make the case that it's a trick question within a trick question. |
Well, I think the purpose of this logic problem was to be able to prove that at least two dogs had to have the same number of hairs, and I think the intended solution was the one I proposed. I suspect it's just poor wording and/or lack of forethought on the creator of the problem that made it impossible to truly proven with the given information. He should have further stipulated that every dog had hair, and that there was more than one dog.
Or maybe the purpose of the logic problem is to force you to realize sometimes you can't come to a solution through logic due to insufficient information. I don't know. |
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