Solution:

Suppose team A has at least two more players than team B. Transfer, X plays every on team B. After the transfer, X plays every player left on team A, which is still more than the number of players originally in team B. So the total number of games played has increased. It follows that to maximize the total number of games played, the size of the teams should not differ by more than 1. Hence we should have 10 players in two of the teams and 9 players in the third team. The total number of games is then 10 x 10 + 10 x 9 + 10 x 9 = 280