IMO Shortlist 2001 problem C3


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2. travnja 2012.
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Define a k-clique to be a set of k people such that every pair of them are acquainted with each other. At a certain party, every pair of 3-cliques has at least one person in common, and there are no 5-cliques. Prove that there are two or fewer people at the party whose departure leaves no 3-clique remaining.
Izvor: Međunarodna matematička olimpijada, shortlist 2001