# Arsenal Collection: Football Logic

##### Age 11 to 16Challenge Level

1. Football Champ? The Year 9 class at Ounsdale High School showed us their method:
• Josh said that to work out the wins, draws and losses we looked at the points and the only possibilities are given below.
• Man City and Chelsea must have drawn because they each had 1 draw.
• Arsenal must have beaten Man City, and Chelsea must have beaten Arsenal.
• Jordan said: the maximum that Man City could have scored in their draw was 2, so it was either 2 - 2 or 1- 1.
• As Chelsea only let in 2 goals in total, and Chelsea must have scored at least one goal against Arsenal, the same between Man City and Chelsea must have ended up 1-1.
• Total number of goals for and against must be equal, because if Arsenal scored against Man City it would count for Arsenal and against Man City, for example.

And their results were as follows:

Teams Games Played  Won  Drawn  Lost Goals For Goals Against  Points
Arsenal 2 1 0 1 5 3 3
Man City 2 0 1 1 2 5 1
Chelsea 2 1 1 0 3 2 4

2. For the Friendly Tournament problem, Szymon from Earl Mortimer College recommended making a table. He explains his method as follows:

Tip 2 says 'Tottenham won their match against Bolton'. Mark this in the table as follows:

 A B C T E F A B C T E F

• Tip 3: 'Arsenal and Everton won the same, odd, number of matches, but Arsenal lost to Everton'. You know that Everton won against Arsenal, so you can plot these straight away. Now, they won either 1, 3 or 5 games each, but it can't be five, because only one person could have won all their matches.
• Tip 5 says Chelsea won only one match, against the other person who won only one as well. We don't know who this is, but there is only one of them, so it can't be Arsenal and Everton, so they must have won 3 of their matches...
If you keep using the tips in this logical way, the eventual table of answers looks as follows:

 A B C T E F A B C T E F

3. Finally, the Qualifying Round problem - this was tough! A bit of careful reading tells you that the results given are only a partial list of results - some games may not have been played yet. Samantha gives her answer as follows:

 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

and the individual results:

A v B: B wins 2-0
A v C: draw 2-2
A v D: A wins 2-0
B v C: draw 2-2
B v D: B wins 1-0
C v D: not played yet.

These solutions were originally submitted for a version of this activity in the context of the Olympics.