F wins all 5.
A wins against B, C and D
E wins against A, C and D
B wins against C and E only
D wins agains B only
C wins against D only
| 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.
Solution to original version by Kenneth Macleod, Forres Academy
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).
| Country | Gold | Silver | Bronze | Total |
|---|---|---|---|---|
| Japan | 9 | 6 | 10 | 25 |
| Italy | 8 | 9 | 10 | 27 |
| France | 7 | 16 | 18 | 41 |
| Team | Played | Won | Drawn | Lost | For | Against | Points |
|---|---|---|---|---|---|---|---|
| A | 3 | 1 | 1 | 1 | 4 | 4 | 3 |
| B | 3 | 2 | 1 | 0 | 5 | 2 | 5 |
| C | 2 | 0 | 2 | 0 | 4 | 4 | 2 |
| D | 2 | 0 | 0 | 2 | 0 | 3 | 0 |
Original solution when this first appeared on the site:
This solution was submitted by Wymondham High School who reasoned their solution in the following way:
To start off we tried to work out the logical answers. For example where it says 'D had no points', it was obvious they had neither a win or a draw.
Then we found out that 'For' and 'Against' columns must add up to the same number. In the end we put 4 in the 'For' column and 2 in the 'Against' column.
At one point we worked out the results to each match. These were:
| A v B | 0 - 2 | B v C | 2 - 2 | C v D | not played |
| A v C | 2 - 2 | B v D | 1 - 0 | ||
| A v D | 2 - 0 |
Here is the finished table of results:
| Team | Played | Won | Drawn | Lost | For | Against | Points |
| A | 3 | 1 | 1 | 1 | 4 | 4 | 3 |
| B | 3 | 2 | 1 | 0 | 5 | 2 | 5 |
| C | 2 | 0 | 2 | 0 | 4 | 4 | 2 |
| D | 2 | 0 | 0 | 2 | 0 | 3 | 0 |
Correct solutions to the problem were also sent in by:
Daniel and David from Archbishop Sancroft High School, Mary from West Flegg Middle School, Ruth from Lynn Grove High School, and students from Necton Middle School and Sheringham High School.