78 replies to this topic

[IntrnilEnfurno]

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?

The answer to this problem is false. There is no concrete solution as there can be an infinite number of people according to the conditions presented.

It is NOT 518 because the rules state that no two people can have the same number of hairs and also that there simply must be more inhabitants that the inhabitant with the highest hairs. It says nothing about ordering. Somebody could have 517 hairs and the next 519 without having to realistically(not that this problem is) have 518 hairs at some point. It could also have 1 million people to 517 hairs. It just says MORE not one more or two more etc. Just MORE. As long as there are more inhabitants than the highest inhabitants hair, the equations is satisfies given that the number of hairs never equals zero.

Jenna

[Martini]

The answer to this problem is false.

No, it's not. Did you read the posts in this thread that explain the answer?

Somebody could have 517 hairs and the next 519 without having to realistically(not that this problem is) have 518 hairs at some point.

No one can have 519 hairs.

It could also have 1 million people to 517 hairs.

How many hairs does the one millionth person have?

Let's use the same conditions but change "No inhabitant has exactly 518 hairs" to "No inhabitant has exactly 2 hairs."

We can have one person with no hair. That works.

We can have two people. One with no hair and the other with one hair.

Can we have three people? Tell me how many hairs each of these three people have on their heads.

[mind0fmadness]

No inhabitants have 518 hairs.. its a trick question.. there is an unlimited number of people.. someone can have 517 or 519 hairs

[smadaus]

This is the most retarded question i ever tried to answer! There is no answer, it can be any number, just because you said no one has exaclty one number of hairs on their doesn't mean they can't have more than that amount. So if you say no one can exactly 50 hairs on their head it doesn't mean they can't have 51 or 52 and so on. Maybe i am just not getting it i don't know but if someone can answer this better than he did please feel free to explain!

[littlefoote]

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?

im with you why not a million hairs? or more?
no way to know 4 sure

[IDoNotExist]

im with you why not a million hairs? or more?
no way to know 4 sure

As stated in the rules of the question, the number of inhabitants must be GREATER than the number of hairs on any single person's head and no one shares the same number of hairs and no one has 518 hairs. Inhabitants> or = hairs+1. This means that in order for there to be 1 million hairs, there must be 1 million and 1 people. The number of hairs plus one. Since no one shares the same number of hairs, and there is no person with 518 hairs, than there must exist a person with 1 million and 1 hairs. if this person exists than there must exist a person with 1 million and 2 hairs. if this person exists than there must exist a person with 1 million and 3 hairs. This could go on indefinitly but the requirements for the question will never be satisfied past 518 people.

[modernjazz]

1st of all, the solution assumes that 0 can be a "number of hairs"
Otherwise there could be no inhabitants, because starting with one hair, you could not have more inhabitants than any inhabitant's hair. 1 person, minimum 1 hair, and already you have number of inhabitants <= any inhabitant's hair, violating this rule: There are more inhabitants than any inhabitant's hair in the town.

One might also think that 0 hairs is not a number of hairs. There are no hairs. A hairless town. What is this "hair" you refer to?

But I digress. We know that 0 is a number in math, so 0 can be a number of hairs. However I would argue that 0 can be thought of as an absence of hair, and not a number of hairs. If everyone is bald, then no one has the same number of "hairs" on their head.

okay, had to get that (hair) off my chest.

Solution seeks maximum number of inhabitants.
0hair = 1 person (more people than hair)
0hair, 1hair = 2 persons (more people than any one head of hair, no two with same number of hairs)
0hair, 1hair, 2 hairs = 3 persons (more people than any one head of hair, no two with same number of hairs)
0hair...517hairs=518 persons (more people than any one head of hair, no two with same number of hairs)
0hair..517hairs, skip 518, 519hairs=519 persons (more people than any any one head of hair no longer true)

518 maximum inhabitants.

Why go consecutively? Why not 1hair, 3hairs, 10hairs etc.? Because there would not be more people than hairs.
0, 1, 2 = 3 people. Consecutive, starting with 0, is the only way. 1hair=1person violates the more people than any head of hair rule.

[Legion]

I would say its infinity+2-1 since there's 1 bald person and 1 more than the number of hairs but there's no one with 518 hairs so that subtracts one from the end total. Although someone with trillions of hairs would look pretty goofy.

[Auramyna]

I just can't believe the amount of people in this topic who have asked for an explanation when so many have already been given, and asked to be proven wrong when they have already been proven wrong. Can people not count up to 3?

One of the reasons it has to be consecutive is because we are looking for the MAXIMUM amount of people. Once you get above 518 people, the amount of inhabitants is equal to the amount of hairs, so there cannot be any more legal inhabitants of the town.