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MathNet 2002 — Part 01 Question 95

Math Olympiad Vault · MathNet 2002 — Part 01

Question 95

$3n$ ($n$ is a positive integer) girl students took part in a summer camp. There were three girl students to be on duty every day. When the summer camp ended, it was found that any two of the $3n$ girl students had just one time to be on duty on the same day.

(1) When $n = 3$, is there any arrangement satisfying the requirement above? Prove your conclusion.