After the close of the soccer season, the final standings for the four teams named A, B, C and D were:
Team | Won | Drawn | Lost | Goals For |
Goals Against |
Points |
---|---|---|---|---|---|---|
A | 3 | 0 | 0 | 7 | 1 | 9 |
B | 1 | 1 | 1 | 2 | 3 | 4 |
C | 1 | 1 | 1 | 3 | 3 | 4 |
D | 0 | 0 | 3 | 1 | 6 | 0 |
Each of the four teams played against one other one time.
Team A beat team B, 3 - 0.
Can you deduce the results of the other five games?
In the standings, the number of points is calculated by mutiplying each win by 3 and each draw by 1. No points are awarded for a loss.
Solution:
Team B beat team D, 2- 0.
Team B drew with team C, 0 - 0.
Team A beat C, 2 - 1.
Team A beat D, 2 - 0.
Team C beat D, 2 - 1.
We see at once from the table that team B beat team D and drew with team C.
As B scored 2 goals to 0 in these games, they must have won 2 - 0 and drawn 0 - 0.
This disposes of B, and leaves three games, C x D, A x D, and A x C to be determined.
Now, A had only 1 goal scored against them (C or D).
D scored only 1 goal, and that must have been against A or C.
Assume that it was against A. In that case, C did not score against A. But C scored 3 goals altogether; therefore these must have been scored against D.
We find D had 6 goals against them : 2 scored by B, as shown, 3 by C (if we assume that D scored versus A), and the remaining goal was scored by A.
But, as we have just assumed, D scored 1 goal against A, the match would have been drawn.
It was won by A, and therefore D could not have scored against A.
Thus, the goal against A must have been scored by C.
And as C scored 3 goals, the other 2 must have been versus D, who must have scored their only goal against C.
Thus, A beat C by 2 - 1 and D by 2 - 0, while C beat D by 2 - 1.
Correctly solved by:
1. Dr. Hari Kishan |
D.N. College, Meerut, Uttar Pradesh, India |
2. Kamal Lohia |
Holy Angel School, Hisar, Haryana, India |
3. Davit Banana | Istanbul, Turkey |
4. Colin (Yowie) Bowey | Beechworth, Victoria, Australia |
5. Ryan Hall |
Parkview Elementary, Chico, California, USA |