GULF 2016 Problem 4

Suppose that four people A, B, C and D decide to play games of tennis doubles. They might first play the team A and B against the team C and D. Next A and C might play B and D. Finally A and D might play B and C. The advantage of this arrangement is that two conditions are satisfied. (a) Each player is on the same team as each other player exactly once. (b) Each player is on the opposing team to each other player exactly twice. Is it possible to arrange a collection of tennis matches satisfying both condition (a) and condition (b) in the following circumstances? (i) There are five players. (ii) There are seven players. (iii) There are nine players.