Here is a well-known logic puzzle: Given that there are more inhabitants of New York City than there are hairs on the head of any inhabitant, and that no inhabitant is totally bald, does it necessarily follow that there must be at least two inhabitants with exactly the same number of hairs?

Here is a little variant of this problem: In the town of Podunk, the following facts are true:
(1) No two inhabitants have exactly the same number of
hairs.
(2) No inhabitant has exactly 518 hairs.
(3) There are more inhabitants than there are hairs on
the head of any one inhabitant.

What is the largest possible number of inhabitants of Podunk?