Define a
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
-clique to be a set of
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
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.
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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.