Question 153
Define a $k$-clique to be a set of $k$ people such that every pair of them know each other (knowing is mutual). At a certain party, there are two or more $3$-cliques, but no $5$-clique. Every pair of $3$-cliques has at least one person in common. Prove that there exists at least one, and not more than two persons at the party, whose departure (or simultaneous departure) leaves no $3$-clique remaining.