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Problem 469

Combinatorics Difficulty 2.0 Find the answer UKMT Grey Kangaroo · United Kingdom · 2020

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

(A) $4$ (B) $5$ (C) $6$ (D) $7$ (E) $8$

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