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4

Part of 2016 Saudi Arabia GMO TST

Problems(1)

16 teams in a football tournament

Source: 2016 Saudi Arabia GMO TST level 4, I p4

8/1/2020
There are totally 1616 teams participating in a football tournament, each team playing with every other exactly 11 time. In each match, the winner gains 33 points, the loser gains 00 point and each teams gain 11 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 44 teams that have the same number of winning matches, the same number of losing matches and the same number of tie matches.
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