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?
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Submitted by pcbouhid
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Rating: 3.0000 (5 votes)
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Solution:
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(Hide)
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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 x 0 and drawn 0 x 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 x 1 and D by 2 x 0, while C won D by 2 x 1.
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