Given that the human head can contain up to several hundred thousand hairs, with a maximum of about 500,000, prove that in New York City, there are two non-bald people who have the same number of hairs on their head. (b) Given that the main hall at Carnegie seats roughly 2,800, in a packed Carnegie Hall performance, there will be two people who have the same first and last initials. (c) Suppose S is a set of n + 1 integers. Prove that there exist distinct a, b ∈ S such that a − b is a multiple of n.