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MathNet 2019-part-05 — 184 problems (EN–VI) Question 124

Math Olympiad Vault · MathNet 2019-part-05 — 184 problems (EN–VI)

Question 124

At a dinner there are $5$ people. Among them there are $7$ pairs of acquaintances (if $A$ knows $B$, then $B$ knows $A$). Prove that there exists a group of $3$ people who know each other.