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# Baldyville

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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.

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• 2 weeks later...
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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.

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• 8 months later...

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.

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• 1 year later...

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.

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