There are $1000$ students in a school. Every student has exactly $4$ friends. A group of three students $ \left \{A,B,C \right \}$ is said to be a friendly triplet if any two students in the group are friends. Determine the maximal possible number of friendly triplets. Proposed by Nikola Velov
Problem
Source: 4th Memorial Mathematical Competition "Aleksandar Blazhevski - Cane"- Junior D2 P6/ Senior D2 P5
Tags: combinatorics, graph theory, double counting, triplets