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 The soccer results (Posted on 2005-06-10)
After the close of a soccer season, with four teams (named A, B, C and D), the final table was:
```TEAM   Won   Drawn Lost     Goals Goals     Points
For   Against
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```
Knowing that the four teams played against each other one time, and that team A beat team B 3x0, can you deduce the results of the other five games?

 See The Solution Submitted by pcbouhid Rating: 3.0000 (5 votes)

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 My Solution | Comment 4 of 20 |

There are 6 games played:

A vs B
A vs C
A vs D
B vs C
B vs D
C vs D

A Beats B 3- 0 (Given).  Since B allowed only 3 goals for all of its games, it's opponents (C & D) scored 0 goals.  B tied C, as they the only teams with ties, so that score was 0 - 0.  B scored 2 goals for the tournament, so B beats D 2 - 0.  Thus far, we have:

A beats B 3 - 0
B ties C 0 -0
B beats D 2- 0

We know that A beats C, and A beats D, as A is undefeated.  A scores 4 goals in these games, (7 total goals less the 3 scored  vs. B) and the opponents score 1.  A must have at least one goal in each game to win, and two goals in the game where the opponent scores 1.  Thus, A scores either 2 in each game or 3 in 1 game and 1 in the other.  If A beats C 3-1 and D 1-0, then C has to beat D 2-0 for C to reach its 3 total goals for.  However this means that A vs D would be a 1 - 1 tie, as A scores 6 goals agains B  & C combined, leaving only 1, and D has no goals against either B or C, leaving 1.  That is impossible.

Flipping it over, if A Beats D 3 - 1 and A beats C 1 -0, then C has to score 3 goals in its game against D to reach it's goals for total.  This is impossible, as D gives up only 6 goals in all of its games, and has already given up 5 against A and B.  Thus, A scored 2 goals each against C and D.  This brings us to this point:

A beats B  3- 0
A beats C  2 - ?
A beats D 2 - ?
B ties C 0 - 0
B beats D 2- 0
C beats D ? - ?

C scores 3 for the tournament and gives up 3.  D gives up 6 for the tournament.  D has given up 2 to A and 2 to B, so C scores 2 vs D.  That leaves 1 for C to score against A.  A only gives up 1 goal in all of its games, which C scored, so D scores nothing against A.  D did score 1 goal in all of its games, which has to be against C, as D was shut out by both A and B.  Thus, the final result:

A beats B 3- 0
A beats C 2-1
A beats D 2 - 0
B ties C 0 - 0
B beats D 2- 0
C beats D 2 -1

 Posted by Jeff Little on 2005-06-10 13:37:41

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