I'm not sure where this goes, but I'll post it here.
Find the smallest integer n > 4 such that there exists a set of n people satisfying the following two conditions:
(i) any pair of acquainted people have no common acquaintance, and
(ii) any pair of unacquainted people have exactly two common acquaintances.
(Note: acquaintance is symmetrical. In other words, if A is acquianted with B, then B is acquainted with A.)