Three teams A, B and C have each played two matches. Three points are given for a win and one point to each team for a draw. The table below gives the total number points and goals scored for and against each team. Fill in the table and find the scores in the three matches.
With so few matches this can be done by trial and error. Can you develop a method which does not use trial and error and which works equally well when there are more teams and more matches?
| Teams | Games Played |
Won | Drawn | Lost | Goals for |
Goals against |
Points |
|---|---|---|---|---|---|---|---|
| A | 2 | 5 | 3 | 3 | |||
| B | 2 | 2 | 1 | ||||
| C | 2 | 3 | 2 | 4 |
In future months we'll publish problems of this sort created and sent in by members. Can you create one? You can have more teams and more matches.