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MathNet 2004 — Part 02 Question 108

Math Olympiad Vault · MathNet 2004 — Part 02

Question 108

$n$ of the townspeople, $n \geq 4$, appears in the telenovela about the events in the conspiracy town. Each group of 3 townspeople conspires against one of the other townspeople. Prove that there is such a citizen that at least $\sqrt[3]{(n-1)(n-2)}$ citizens are involved in a conspiracy against him.