Funny group of students
Source: Southern Summer School, gr. 12
July 9, 2017
combinatoricsgraph theory
Problem Statement
In a summer school, there are students. It is known that, among these students,
i. If two ones are friends, then they don't have any common friends.
ii If two ones are not friends, then they have exactly two common friends.
1. Prove that must be a perfect square.
2. Determine the smallest possible value of .