MathDB

In a school with some students, for any three student, there exists at least one student who are friends with all these three students.(Friendships are mutual) For any friends

A

and

B

, any two of their common friends are also friends with each other. It's not possible to partition these students into two groups, such that every student in each group are friends with all the students in the other gruop. Prove that any two people who aren't friends with each other, has the same number of common friends.(Each person is a friend of him/herself.)

Problem Statement