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National and Regional Contests
Saudi Arabia Contests
Saudi Arabia GMO TST
2016 Saudi Arabia GMO TST
2016 Saudi Arabia GMO TST
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Saudi Arabia GMO TST
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16 teams in a football tournament
There are totally
16
16
16
teams participating in a football tournament, each team playing with every other exactly
1
1
1
time. In each match, the winner gains
3
3
3
points, the loser gains
0
0
0
point and each teams gain
1
1
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
4
4
teams that have the same number of winning matches, the same number of losing matches and the same number of tie matches.
3
6
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4
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