78 replies to this topic

[Snowball]

The question was invalid! Why would anyone name it "baldyville" if anyone had hair? INVALID! INVALID! INVALID!

[NateET]

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.

[sk8rkat]

i kno i kno- 518 it is so easy-

[Lost in space]

I am not bald, I am SOLAR POWERED!

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?

Spoiler for Am i missing something

TWO ..... one with 1 hair and one with none, though 2 with no hair would be ideal for it to be Baldyville.

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

[Sean-in-Oz]

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!

[Sandeep]

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)????

[Yugi]

[quote name='rookie1ja' date='Mar 30 2007, 04:40 PM' post='29']
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.

[belwood]

Maybe this is a case of splitting-hairs regarding English usage (pardon the pun), but as a possible clarification, consider dropping the word "exactly" from condition 2. The word appears to introduce ambiguity.

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

[tink]

it depends on how you look at it there isnt 1 that has exactly 518 hairs but maybe more maybe less there is not enophe info to ecurutly make an answer

[Smaptastic]

Flawed logic. The answer is infinity-1.

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.