Question 189
Every two members of a certain society are either friends or enemies. Suppose that there are $n$ members of the society, that there are exactly $q$ pairs of friends, and that in every set of three persons there are two who are enemies to each other. Prove that there is at least one member of the society among whose enemies there are at most $q \cdot\left(1-\frac{4 q}{n^{2}}\right)$ pairs of friends.