16 teams in a football tournament
Source: 2016 Saudi Arabia GMO TST level 4, I p4
August 1, 2020
combinatoricsgame
Problem Statement
There are totally teams participating in a football tournament, each team playing with every other exactly time. In each match, the winner gains points, the loser gains point and each teams gain point for the tie match. Suppose that at the end of the tournament, each team gains the same number of points. Prove that there are at least teams that have the same number of winning matches, the same number of losing matches and the same number of tie matches.