[rookie1ja]

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 in town than hairs on any individual inhabitant's head.

What is the highest possible number of inhabitants?

Spoiler for Solution:

Baldyville - solution
There can live maximum of 518 people in the town. By the way, it is clear that one inhabitant must by baldy, otherwise there wouldn’t be a single man in the town.

Spoiler for old wording:

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?

[netwebdave]

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

[jason210]

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.

[thephife]

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.'

[mynameisjjonas]

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

[ggsarah]

yea well explained thephife..

[sdy4444]

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

[toxa26]

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?

[infomaniac.nick]

Quote

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

[Fysh]

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