Ana, Beatriz, Carlos, Diego and Emilia play a chess tournament
Source: V May Olympiad (Olimpiada de Mayo) 1999 L1 P5
September 17, 2022
combinatoricsalgebra
Problem Statement
Ana, Beatriz, Carlos, Diego and Emilia play a chess tournament. Each player faces each of the other four only once. Each player gets points if he wins the match, point if he draws and point if he loses. At the end of the tournament, it turns out that the scores of the players are all different. Find the maximum number of ties there could be in the tournament and justify why there could not be a higher number of ties.