Question 144
In a soccer tournament each team plays exactly one game with all others. The winner gets 3 points, the loser zero and each team gets 1 point in case of a draw.
It is known that $n$ teams ($n \ge 3$) took part in a tournament and the final classification is given by an arithmetical progression of points, the last team having only 1 point.
a) Prove that this is not possible in the Championship of the Republic of Moldova (with $n=12$).
b) Find all values of $n$ and all configurations when this is possible.
It is known that $n$ teams ($n \ge 3$) took part in a tournament and the final classification is given by an arithmetical progression of points, the last team having only 1 point.
a) Prove that this is not possible in the Championship of the Republic of Moldova (with $n=12$).
b) Find all values of $n$ and all configurations when this is possible.