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. Here are the results given by Lim Zi Heng, Goh Wei Ming, Chong Ching Tong, Chan Hei Leong, Chen Wei Jian and Ng Yan Shun from River Valley High School, Singapore, Kenneth Macleod, Forres Academy and Daniel Pick, Bourne Grammar School.
| Teams |
Games Played |
Won | Drawn | Lost |
Goals for |
Goals against |
Points |
|---|---|---|---|---|---|---|---|
| A | 2 | 1 | 0 | 1 | 5 | 3 | 3 |
| B | 2 | 0 | 1 | 1 | 2 | 5 | 1 |
| C | 2 | 1 | 1 | 0 | 3 | 2 | 4 |
The scores are A versus B = 4-1, B versus C = 1-1 and C versus A= 2-1. Kenneth explained how, given the information in the table below, he got all the results (being football mad he said).
| 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 |
Team A have obviously won 1 game and lost 1 game because they have three points which means they have won 1 game and because all the teams have played 2 games, they have lost a game too. If team A had drawn a game they would have 4 points. So team A beat team B(4-1) and lost to team C(1-2).
With 3 matches there are few possibilities. With more teams and more matches you can use algebra to find the missing information.
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.