Sam had never fully understood the points system in soccer (football), and felt that the scoring of goals should be encouraged. His idea is that 10 points should be awarded for a win, 5 points for a draw and 1 point for each goal scored, whatever the result of the match.
This was tried with three teams, Hubs, Dins and Rungs.
Each team scored at least one goal in every mach and no team played another more than once.
Hubs scored 8 points, Dins 14 points and Rungs scored 9 points.
Find the score in each match.
The possibilities are:
(wins, draws, goals)
Hubs: (0, 0, 8) or (0, 1, 3)
Dins: (0, 0, 14) or (0, 1, 9) or (0, 2, 4) or (1, 0, 4)
Rungs: (0, 0, 9) or (0, 1, 4)
If there were 3 games, then there would be 30 points
for wins and draws, leaving just 1 point for goals,
so that is not possible, since each team scored in each game.
Thus, there were only 2 games,
yielding 20 points for wins and draws, 11 for goals,
which reduces the possibilities to
Hubs: (0, 1, 3)
Dins: (0, 2, 4) or (1, 0, 4)
Rungs: (0, 1, 4)
The Hubs had a draw (and maybe a loss).
The Dins had 2 draws or a win and no other match.
The Rungs had a draw (and maybe a loss)
If the Dins had 2 draws, then both games were draws,
but that is not possible since total goals was 11, which is odd.
So the Dins had a win against one of the others,
and the other game was a draw between the Hubs and the Rungs.
The score of the Hubs-Rungs draw then was either 1-1, 2-2, or 3-3
Since the Rungs scored more goals than the Hubs, they
are the ones who lost to the Dins, and the Hubs, only playing once,
scored all 3 goals in that game, equalling the Rungs.
The Dins scored all 4 of their goals in their only game, where
the Rungs scored one additional goal.
