China Girls' Mathematical Olympiad

Question

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.

Accepted Answer

(1) When n = 3, there is an arrangement satisfying the requirement. Now the concrete arrangement is given as follows (Denote the nine girl students by 1, 2, , 9): (1, 2, 3), (1, 4, 5), (1, 6, 7), (1, 8, 9), (2, 4, 6), (2, 7, 8), (2, 5, 9), (3, 4, 8), (3, 5, 7), (3, 6, 9), (4, 7, 9), (5, 6, 8).