Question 2
(USA 3) At a party attended by $n$ married couples, each person talks to everyone else at the party except his or her spouse. The conversations involve sets of persons or cliques $C_1,C_2,\ldots,C_k$ with the following property: no couple are members of the same clique, but for every other pair of persons there is exactly one clique to which both members belong. Prove that if $n\ge4$, then $k\ge2n$.