BALKAN-SL 2010 C1

In a soccer tournament each team plays exactly one game with all others. The winner gets $3$ points, the loser gets $0$ and each team gets $1$ point in case of a draw. It is known that $n$ teams ( $n \geq 3$ ) participated in the tournament and the final classification is given by the arithmetical progression of the points, the last team having only 1 point. [list=a] [] Prove that this configuration is unattainable when $n=12$ [] Find all values of $n$ and all configurations when this is possible [/list]