Baldyville

[Guest]

The criteria for determining any number at all is actually not met. It stipulates that no inhabitant has EXACTLY 518 hairs, it doesn't stipulate that no inhabitant had more or less than 518 hairs. Is it me or are there a lot of people making something out of this that just isn't there? Spell check could stand to be used on this also.

[Guest]

Does this include moustaches, beards, ear & nose hairs?

[Guest]

Where does this imply that the # of hairs has be be in increments of 1.

There might not be anyone with 1 - 50 hairs on their head.

Therefore unless it is stipulated that the # of hairs is incremented by 1 from person to person, then there could be any number of people.

[Guest]

saying dat nbdy has xctly 518 hair on their head dsnt mean people cannot ve 519 ,517 or for cat matter 520

[Guest]

To Credels:

The teaser states "on their head"

[Guest]

It blows me away to see how many people don't get it.

The rules

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.

In regards to the hair count having to be continuous:

No it isn't stated directly, but it is derived and is absolutely true. This is due to rules 3 and 1.

To understand this; start by picking any number to represent the number of hairs from the inhabitant with the most hairs. Lets use 10 to keep it simple.

Since this inhabitant has 10 hairs, there must be at least 11 inhabitants (rule 3).

And according to rule 1, the numbers for each of the inhabitants hair count must be unique.

We can now prove that there can only be 11 inhabitants and the number of hairs must be continuous.

If there are more than 11 inhabitants and the maximum number of hairs is 10 (value picked above) then there must be two with the same number of hairs (by the way: zero is a number, 7th grade math, maybe earlier) which violates rule 1. If you dispute this, I would like to know how you manage to get more than 11 numbers from 0 to 10 without duplicating a number. (Counting implies integers, preschool math or thereabouts). We therefor know that if the person with the most hairs has 10 hairs, there must be 11 people, no more (just shown), no less (rule 3).

Since we know that if the person with the most hairs has 10 hairs, there are 11 people (above). If there are 11 people and the max number of hairs is 10 (as stated), there can't be any gaps in the sequence. Again, I don't know how you can get 11 numbers between 0 and 10 inclusive and have a gap.

Now, if there is a number of hairs that is not allowed to exist, the sequence must stop since there can't be any gaps. Therefore if there can't be anyone with 518 hairs, there can't be anyone with more either. This means that there can be any number of inhabitants less that 518 except the problem is asking for the maximum number which is 518.

If this, along with the previous explanations, doesn't prove it, I must condeed that there are those who refuse to see the forest for the trees. i.e. too fixated on what they want rather than what is.

[Guest]

there can be no more than 518 people (0-517 hair)

[Guest]

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?

There is no rule stating that there the people in the town have specific numbers on their head it only says they don't have the same number of hairs as any one else. it also says there are more inhabitants that any inhabitants hair. that means there can be 530 people in the town as long as one person is bald no one has 518. Because even if you had 700 people with hair you would still have one man with no hair always keeping the number of people higher than the numbers of hair.

[rookie1ja]

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?

There is no rule stating that there the people in the town have specific numbers on their head it only says they don't have the same number of hairs as any one else. it also says there are more inhabitants that any inhabitants hair. that means there can be 530 people in the town as long as one person is bald no one has 518. Because even if you had 700 people with hair you would still have one man with no hair always keeping the number of people higher than the numbers of hair.

if you had 700 people then:

1. No two inhabitants have the same number of hairs on their head ... so 0 hair (1st person), 1 hair (2nd person) ... 699 hairs (700th person) ... each one - out of 700 - will have unique number of hairs

2. No inhabitant has exactly 518 hairs ... oops - I have to take this into account for the line above ... so so 0 hair (1st person), 1 hair (2nd person) ... no one with 518 hairs ... 700 hairs (700th person)

3. There are more inhabitants than any inhabitant's hair in the town ... so there would be 700 people and the last one has 700 hairs ... soooo there can't be 700 of them

[Guest]

yes but on a smaller scale if there was a bald guy and no one could have exactly 6 hairs how many people are in the town as long as there were more people than the number of hairs

baldy-1 person

one hair+ baldy= 1 hair=2 people

one hair+ 2 hair+ baldy=2 hair=3 people

one hair+ 2 hair + 3 hair+ baldy=3 hair=4 people

one hair + 2 hair + 3 hair + 4 hair+baldy=4 hair= 5 people

one hair + 2 hair + 3 hair + 4 hair+ 5 hair+baldy= 5 hair=6 people

no one can have 6 hairs so we are still dealing with 6 people

okay im wrong but if you read this you are no longer sure that HAIR is a real word//haha

[Guest]

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?]

With all of the discussion on this one, it surprises me no one caught this. Why did no one notice that the "No inhabitant has exactly 518 hairs" does not specify that those hairs need to be on their head? When you take this into account, you can have an infinite number of body and head hair combinations, as long as they don't equal 518. Therefore, this puzzle does not have an answer because it grows to infinity.

Example:

I am bald. I am the only bald guy in town.

I have 1000 hairs on my palms.

This meets the both Criteria 1 and Criteria 2 unless I am mistaken.

Criteria 3 states that (inhabitants > number of hair on a person).

Therefore the number of inhabitants in my example is any number greater than 1000.

Correct me if I am wrong, but I do not think that I am.

[rookie1ja]

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?]

With all of the discussion on this one, it surprises me no one caught this. Why did no one notice that the "No inhabitant has exactly 518 hairs" does not specify that those hairs need to be on their head? When you take this into account, you can have an infinite number of body and head hair combinations, as long as they don't equal 518. Therefore, this puzzle does not have an answer because it grows to infinity.

Example:

I am bald. I am the only bald guy in town.

I have 1000 hairs on my palms.

This meets the both Criteria 1 and Criteria 2 unless I am mistaken.

Criteria 3 states that (inhabitants > number of hair on a person).

Therefore the number of inhabitants in my example is any number greater than 1000.

Correct me if I am wrong, but I do not think that I am.

actually, there was 1 person in the village who had some hair (of his dog) left on his head ... I forgot to mention that as well ... and now I remember, one old lady had a wig (from not her own hair)

[Guest]

Never mind my previous post. I thought about it over the weekend, and my point was invalid.

[Guest]

Spenglers example is fantastic. For those of you confused by the problem-solving approach here (i.e. the consecutive ordering) I'd suggest doing some research on the "well-ordering principle". I did a cursory search and found pages that probably wouldn't appeal to most; however, this is an extremely powerful tool logicians and mathematicians use when attacking problems like this one that deals with sets.

[Guest]

Spenglers example is fantastic. For those of you confused by the problem-solving approach here (i.e. the consecutive ordering) I'd suggest doing some research on the "well-ordering principle". I did a cursory search and found pages that probably wouldn't appeal to most; however, this is an extremely powerful tool logicians and mathematicians use when attacking problems like this one that deals with sets.

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!

Edited January 15, 2008 by Quinten27

[Guest]

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

[Guest]

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.

[Guest]

i kno i kno- 518 it is so easy-

[Guest]

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?

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.

[Guest]

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!

[Guest]

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)????

[Guest]

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.

[Guest]

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

[Guest]

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

[Guest]

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.