CGMO 2002 Problem 2

There are $3n, n \in \mathbb{Z}^+$ girl students who 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 $3n$ 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 yor conclusion.

(2) Prove that $n$ is an odd number.