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# Baldyville

### #41

Posted 24 January 2008 - 06:18 PM

### #42

Posted 22 February 2008 - 05:30 PM

Hmmmmm, so if a man has one hair on his head, and he goes to the barber and gets the hair cut in half, does that mean the man now has half a hair on his head? Using increments of halves would allow for an infinite town population!

Yes, because there was any requirement on the /length/ of the air, so once the hair is below that length, it counts as a fraction of a hair, instead of still being a hair. Because when you're counting hairs on someone's head, you'll go, 'Oh, that one is half-length, so I count it as half a hair.'

Can people stop being stupid when intelligent questions are being asked? It ruins the moment.

### #43

Posted 22 February 2008 - 09:51 PM

### #44

Posted 05 March 2008 - 09:34 AM

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 than any inhabitant's hair in the town.

What is the highest possible number of inhabitants?

Did not factor syrups (wigs) into the great sceme of things.

### #45

Posted 05 March 2008 - 11:26 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.

Aha, I was just getting ready to agree with Jason and others that the puzzle should have stated, "No inhabitant has 518 or more hairs on his head." However the original answer is correct.

"There are more inhabitants than any inhabitant's hair in the town" is the reason. Others have suggested that you could have some inhabitants that have more than 518 hairs -- not true. Say you have one bloke with 519 hairs. This last rule means that there must be AT LEAST 520 inhabitants. And there is no way to get there. Since we have eliminated 518 as a possibility, even if we use every possible number, we still won't ever get to MORE inhabitants that the hairs on the last bloke's head.

To prove this let's assume the puzzle was for nobody had exactly TWO hairs.

Nobody has two, therefore the MAXIMUM number of residents is two. One bloke has one hair and the other is bald.

If you are still arguing that a THREE haired bloke will meet the conditions, then who are the residents?

Baldy is the first, One Hair is the second, Three Hair is the third . . . but while we have now created more than TWO residents, we have a problem with the last condition. The population has to be greater than any inhabitant's hairs. So to meet the last condition (we now have a three haired man!) we need a fourth . . . How about FOUR HAIRED man? Sure but now we need a population of more than FIVE . . . . can't do that ever.

Easy when you plug in easier numbers, but still a good logic problem!

### #46

Posted 11 March 2008 - 11:50 AM

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.'

Well... Taken, but why can not ther be someone who has, say 519 hair, & he stands in the 519th position (taking place of the missing person with that missing 518th hair)????

### #47

Posted 15 March 2008 - 08:06 PM

**Baldyville**- Back to the Logic Puzzles

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 than any inhabitant's hair in the town.

What is the highest possible number of inhabitants?

Acording to the information given and the conditions, there can be an infinate number of people in town. Since our # system goes on forever and it never says how big the town is, it's possible that there can be an infinate amount.

### #48

Posted 19 March 2008 - 06:37 PM

How about

2. No inhabitant has 518 hairs.

?

This implicitly requires that no inhabitant have MORE THAN or EXACTLY 518 hairs with less ambiguity (it's a puzzle, so we don't want to give away too much!)

My 2c

### #49

Posted 20 March 2008 - 02:46 AM

### #50

Posted 24 March 2008 - 01:27 PM

No one has EXACTLY 517 hairs. But you can have someone with 0, 1, 2,...516, 518.... eleventy billion... infinite

So given that your question allows for infinite hairs, there can be infinity-1 people.

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