There are 4 teams in a soccer tournament. Each team plays each of the other teams exactly once. In each match, the winner receives 3 points and the loser receives 0 points. In the case of a tie, both teams receive 1 point. After all the matches have been played, which of the following total number of points is it impossible for any team to have received?

Given that there are 4 teams and Each team plays each of the other teams exactly once, then each team plays 3 matches. The possible points after 3 matches are:

0: 3 lost

1: 2 lost, 1 tied

2: 2 tied, 1 lost

3: 3 tied

4: 1 won, 1 lost, 1 tied

5: 1 won, 2 tied

6: 2 won, 1 lost

7: 2 won, 1 tied

9: 3 won

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francocanacari francocanacari · Answer 2 · 2021-09-21T19:09:59+02:00

The answer is 8 points.

Since there are 4 teams in a soccer tournament, and each team plays each of the other teams exactly once, and in each match, the winner receives 3 points and the loser receives 0 points, while in the case of a tie, both teams receive 1 point, to determine, after all the matches have been played, which total number of points is it impossible for any team to have received, the following mathematical logical reasoning must be performed:

0 points = 3 losses = possible
1 point = 1 draw, 2 losses = possible
2 points = 2 draws, 1 loss = possible
3 points = 1 win, 2 losses or 3 draws = possible
4 points = 1 win, 1 draw, 1 loss = possible
5 points = 1 win, 2 draws = possible
6 points = 2 wins, 1 loss = possible
7 points = 2 wins, 1 draw = possible
8 points = impossible, it takes at least 4 matches to achieve that combination
9 points = 3 wins = possible

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