MathDB

In the parliament of Nekurnekadzeme, all activities take place in commissions, which consist of exactly three members. The constitution stipulates that any three commissions must have at least five members. We will call a family of commissions a clique if every two of them have exactly two members in common, but if any other commission is added to this family, this condition is no longer fulfilled. Prove that two different cliques cannot have more than one commission in common.

Problem Statement