ISL 2007 C6
In a mathematical competition some competitors are friends; friendship is always mutual. Call a group of competitors a clique if each two of them are friends. The number of members in a clique is called its size. It is known that the largest size of cliques is even. Prove that the competitors can be arranged in two rooms such that the largest size of cliques in one room is the same as the largest size of cliques in the other room. (Russia)
Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.
Official text: IMO 2007 Shortlist booklet, page 35.
Solutions
Official solution Solution 1 by the IMO Problem Selection Committee
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