MathDB

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.
[*] Prove that this configuration is unattainable when

n=12

[*] Find all values of

n

and all configurations when this is possible

Problem Statement