Question 140
Eight teams participated in a soccer tournament, and each pair of teams have played exactly once. It appeared that if two teams $A$ and $B$ played a draw then the resulting numbers of points of $A$ and $B$ are different. Find the greatest possible number of draws in this tournament. (Each win is worth 3 points, each draw is worth 1 point, and each lose is worth 0 points.) (S. Tokarev)