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Found problems: 1

2022 Canadian Mathematical Olympiad Qualification, 1
Tags: graph theory , repecharge , wehfuwhuwhue
Let $n \geq 2$ be a positive integer. On a spaceship, there are $n$ crewmates. At most one accusation of being an imposter can occur from one crewmate to another crewmate. Multiple accusations are thrown, with the following properties: • Each crewmate made a different number of accusations. • Each crewmate received a different number of accusations. • A crewmate does not accuse themself. Prove that no two crewmates made accusations at each other.