KMO 2009 Problem 4

There are $n ( \ge 3)$ students in a class. Some students are friends each other, and friendship is always mutual. There are $s ( \ge 1 )$ couples of two students who are friends, and $t ( \ge 1 )$ triples of three students who are each friends. For two students $x, y$ define $d(x,y)$ be the number of students who are both friends with $x$ and $y$ . Prove that there exist three students $u, v, w$ who are each friends and satisfying $$d(u,v) + d(v,w) + d(w,u) \ge \frac{9t}{s} .$$