8 chess players
Source: All-Russian MO 2009 Regional 9.8
August 27, 2024
combinatorics
Problem Statement
8 chess players participated in the chess tournament and everyone played exactly one game with everyone else. It is known that any two chess players who play a draw with each other ended up scoring different numbers of points. Find the greatest possible number of draws in this tournament. (For winning the game the chess player is awarded point, for a draw points, for defeat points.)