MathDB

There are

15

boys and

15

girls in the class. The first girl is friends with

4

boys, the second with

5

, the third with

6

, . . . , the

11

th with

14

, and each of the other four girls is friends with all the boys. It turned out that there are exactly

3 \cdot 2^{25}

ways to split the entire class into pairs, so that each pair has a boy and a girl who are friends. Prove that any of the friends of the first girl are friends with all the other girls too. G.M.Sharafetdinova

Problem Statement