I'm not sure where this goes, but I'll post it here.

Find the smallest integern> 4 such that there exists a set ofnpeople 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.)