These are the conditions in Baldyville:

No two inhabitants have the same number of hairs on their head.
No inhabitant has exactly 518 hairs.
There are more inhabitants in town than hairs on any individual inhabitant's head.
What is the highest possible number of inhabitants?

• 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.'
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