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2001 IMO Shortlist Problems/C3

Revision as of 17:21, 20 August 2008 by Minsoens (talk | contribs) (New page: == Problem == Define a <math>k</math>-<i>clique</i> to be a set of <math>k</math> people such that every pair of them are acquainted with each other. At a certain party, every pair of 3-cl...)
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Problem

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.

Solution

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Resources

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