There are five teams in the local league and each team plays each of the others once a season. The table of stats kept by one of the members is as follows:
Won Drawn Lost Goals Goals
for against
Arnsley 2 1 1 2 2
Boldham 3 1 0 2 1
Cleeds 1 3 0 1 0
Drochdale 1 2 1 1 1
Erby 1 0 3 1 3
But three of his numerical entries in the table are wrong.
What were the scores of Arnsley's four games? ... and the other teams' games?
Total games won (TW) must be equal to total games lost (TL). Moreover, total games won, lost and drawns must be equal to total games x 2
TW = TL
TW + TD + TL = 4 x 5 = 20 -> TW + TD + TW = 20 ->
TW + TD/2 = 10
Also, TD must be even (for every one team getting a drawn, there is the also the team it played against).
As it is: TW = 8, TD = 7, TL = 5
For Boldham to have won 3 games without losing at any other game, its Goals for have to be at least by 3 greater than its goals against (one extra goal per game won). But that is not the case: 2 - 1 = 1.
So, if the goals are correct (which seems like it, since total goals against = total games for = 7), Boldham could have won at most 1 game, which makes TW = 6. If the goal Boldham has taken cost it a game, then its games lost becomes 1 -> TL = 6 = TW. The remaining game of Boldham is obviously a draw.
Finally:
A 2 1 1 2 2
B
1 2 1 2 1
C 1 3 0 1 0
D 1 2 1 1 1
E 1 0 3 1 3
which is correct (with bold the corrections).
The scores are (all scores are as if the team was playing in its own seat)
A 1-0 1-0 0-0 0-2
B 2-0 0-0 0-0 0-1
C 1-0 0-0 0-0 0-0
D 1-0 0-0 0-0 0-1
E 1-0 0-1 0-1 0-1
No Subject
