IMO Shortlist 1987 problem 2

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Dodao/la: arhiva
2. travnja 2012.
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, \cdots, 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 \geq 4, then k \geq 2n.

Proposed by USA.
Izvor: Međunarodna matematička olimpijada, shortlist 1987