Question 146
Eight players participated in a chess tournament, and each pair of players have played exactly once. It appeared that if two players $A$ 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 $1$ point, each draw is worth $\frac{1}{2}$ points, and each lose is worth $0$ points.) (S. Tokarev)