Question 17
A3 (FIN). A game is played by $n$ girls ($n\ge2$), everybody having a ball. Each of the $\binom n2$ pairs of players, in an arbitrary order, exchange the balls they have at that moment. The game is called nice if at the end nobody has her own ball, and it is called tiresome if at the end everybody has her initial ball. Determine the values of $n$ for which there exists a nice game and those for which there exists a tiresome game.