Question 21
There are totally 16 teams participating in a football tournament; each team playing with every other exactly 1 time. In each match, the winner gains 3 points, the loser gains 0 point and each team gains 1 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 4 teams that have the same number of winning matches, the same number of losing matches and the same number of tie matches.