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# Baldyville

78 replies to this topic

### #1 rookie1ja

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Posted 30 March 2007 - 03:40 PM

Baldyville - Back to the Cool Math Games
These are the conditions in Baldyville:

1. No two inhabitants have the same number of hairs on their head.
2. No inhabitant has exactly 518 hairs.
3. There are more inhabitants in town than hairs on any individual inhabitant's head.

What is the highest possible number of inhabitants?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.
Pls visit New Puzzles section to see always fresh brain teasers.

Spoiler for Solution

Spoiler for old wording

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### #2 netwebdave

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Posted 06 May 2007 - 04:45 AM

What if inhabitant 519 had a split end that broke off? Would that be exactly one hair or a partial hair?
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### #3 jason210

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Posted 22 May 2007 - 08:24 PM

There is no correct answer to this question. Just because no one has exactly a certain number of hairs, doesn't mean that somone doesn't have more hair then that. you can say x is not = to 386 but that does not mean that x is not equal to 387, 388, 389 etc.
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### #4 thephife

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Posted 04 June 2007 - 12:24 PM

no, 518 is the correct answer. take as an example, that there are 519 people in the town. to be orderly, we line them up by the number of hairs on their heads from 0-517. thats 518 people, but by our conditions, the last person may not have 518 hairs because that was specified. it was also specified that there are more people than hairs so the the last person must have less than 519 hairs. yet, if that were true there would be a repeat in number of hairs since we've already accounted for people from bald to 517 hairs and 518 is off limits. so for 519 or more, to paraphrase a quote, 'no soup for us.'
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### #5 mynameisjjonas

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Posted 07 June 2007 - 05:26 AM

Good explanation. I didn't get it either, but now I do
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### #6 ggsarah

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Posted 22 June 2007 - 04:41 PM

yea well explained thephife..
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### #7 sdy4444

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Posted 25 June 2007 - 06:27 AM

i dont understand why there cannot be 520 people, even with your explanation of 519
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### #8 toxa26

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Posted 27 June 2007 - 01:28 PM

I have exactly the same issue with this puzzle as sdy4444. Why cant someone have 1000 hairs? Nowhere does it say that you cant have MORE then 518. It says you cant have that exact number ... Am I being dense or does this puzzle need some work?
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### #9 infomaniac.nick

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Posted 28 June 2007 - 04:03 PM

I have exactly the same issue with this puzzle as sdy4444. Why cant someone have 1000 hairs? Nowhere does it say that you cant have MORE then 518. It says you cant have that exact number ... Am I being dense or does this puzzle need some work?

If someone had 1000 hairs, there would need to be at least 1001 people.
the would have no hairs, the 2nd would have one the 3rd two... the 518th would have 517, the 519th can't have 518 hairs (as stipulated in the rules) but their can't be as many people in the town than the greateast number of hairs on a head. hence 518 is the greatest number of people in the town!

QED
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### #10 Fysh

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Posted 02 July 2007 - 05:11 AM

The aside in the solution makes the given solution false. If one inhabitant is bald, then any number of non-repeating hair counts would equal the population of the city. If no one is bald, and there is no one with 518 hairs, then there could be an infinite number of people in the town, given that the person with the most hair has one less hair the the number of people in town
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