## 6. Mopmet

In a new sport called mopmet, 19 teams compete, each playing one match against every other team. In case of a win by one of the teams, the winning team gets 4 points, while the losing team gets no points. In case of a draw, each of the two teams gets 1 point. All teams at the tournament have accumulated a total of 600 points. How many matches ended with one team winning?

## Result: 129
First method. Suppose each two teams play twice, once with one team as the home team, and the other time with the other team as the home team. We can choose the home team in 19 ways, and the away team in 18 ways. This means that the double number of matches is $19 \cdot 18=342$, so the number of matches is $342: 2=171$.