Football League

Question

In a football league matches, 10 points are awarded for a win, 5 points for a draw and 1 point for each goal scored by the team.

A, B & C are eventually all going to play each other once, and after some (or perhaps all) of the matches have been played A has 8 points, B has 2 points and C has 22 points. It is interesting to notice that each side scored at least 1 goal in every match.

Find the points (& goals scored) of all the matches played.

Answer 1

1. Team B has 2 points only. It means the team has scored 2 goals and lost its game. The team has played one game only and lost to C.
2. Team A has 8 points. It means the team has no wins (less than 10 points), has 1 draw worth of 5 points plus scored 3 goals. The only game was against C and resulted 3:3.
3. Team C has 22 points. It means the team has 1 win +1 draw + 7 goals. Its not possible to have 2 wins, as in this case team should have scored min 4 goals and get min of 24 points (20 for 2 wins and 2x2 for goals). Since the draw was against A and score was 3:3, the win was against B with the score of 4:2.

There was 2 games only:
A-C = 3:3
C-B = 4:2