Soccer

Dec 2019
52
1
ok
Four soccer teams from the cities Icetown, Frostville, Glacierhampton and Coldbury have participated in the Xmas soccer tournament. During this tournament, each team played exactly one match against each of the other three teams. A win yields three points, a draw one point, and a loss zero points. No two of these six matches ended with the same result. (For example: if some match ended in 3:4 then none of the other five matches ended with 4 goals for one team and 3 goals for the other team.) Here is the final of table of the tournament:

Icetown - 2 wins, 0 draws, 1 loss - 5 Goals and 1 Goals against - 6 points
Frostville - 2 wins, 0 draws, 1 loss - 3 Goals and 5 Goals against - 6 points
Glacierhampton - 1 win, 0 draws, 2 losses - 5 Goals and 6 Goals against - 3 points
Coldbury - 1 win, 0 draws, 2 losses - 4 Goals and 5 Goals against - 3 points

Which of the following statements is true?
1. Cold. won its match against Glac. 1:0
2. Cold. lost its match against Glac. 0:1
3. Cold. won its match against Glac. 2:0
4. Cold. lost its match against Glac. 0:2
5. Cold. won its match against Glac. 3:0
6. Cold. lost its match against Glac. 0:3
7. Cold. won its match against Glac. 2:1
8. Cold. lost its match against Glac. 1:2
9. Cold. won its match against Glac. 3:1
10. Cold. lost its match against Glac. 1:3
 
May 2013
94
10
Let's see how much we can deduce.
Icetown lost once, with only 1 goal against. This means they got 0:1 against some team.
Frostville got 2 wins with only 3 goals, so they either went 2:0 or 2:1 along with a 1:0 score.
Unfortunately, this breaks the rules. I see no clear way around this.
 

skipjack

Forum Staff
Dec 2006
21,321
2,386
It doesn't break the rules.
Icetown: 3, Glacierhampton: 0
Icetown: 2, Coldbury: 0
Frostville: 1, Icetown: 0
Frostville: 2, Coldbury: 1
Glacierhampton: 4, Frostville: 0
Coldbury: 3, Glacierhampton: 1

Statement 9 is true.
 
Dec 2019
52
1
ok
It doesn't break the rules.
Icetown: 3, Glacierhampton: 0
Icetown: 2, Coldbury: 0
Frostville: 1, Icetown: 0
Frostville: 2, Coldbury: 1
Glacierhampton: 4, Frostville: 0
Coldbury: 3, Glacierhampton: 1

Statement 9 is true.
So basically what I did was this:

Icetown has to lose (0,1) as they only lose one time with one goal being allowed.
They can't win (4,0) as that would make the other match (1,0) which is not allowed (No match ends with the same result).
So Icetown wins (2,0) and (3,0) and loses (0,1)

The only way Frostville can obtain 3 points in 2 matches is for the winning scores to be 2 and 1.
Since Icetown already had a (2,0) match, Frostville wins (2,1) and (1,0). In total, Frostville allowed 5 goals,
so that means they lost a match (0,4)
With this information, you can conclude that Frostville beats Icetown (1,0).

So now I'm wondering whether Glacierhampton or Coldbury wins the (4,0) match against Frostville.
If Coldbury won the match, that would mean their other matches would be (0,0)/(0,5) or (0,1)/(0,4) or (0,2)/(0,3)
(0,0) is impossible because there are no draws.
(0,4) is impossible because no match ends with the same result.
However, I don't know if (0,2)/(0,3) is possible. If it isn't, then Glacierhampton definitely wins the (4,0) match.

Can you help me with this? This might be really easy but I just can't see it.
 

skipjack

Forum Staff
Dec 2006
21,321
2,386
You were correct that Icetown had a (0, 1) loss, a (2, 0) win and a (3, 0) win.

You were also correct that as Frostville had a winning score of (1, 0), this was for their match with Icetown, and their remaining scores were (2, 1) and (0, 4).

If Frostville lost (0, 4) to Coldbury, Coldbury's losses were (0, 2) and (0, 3) to Glacierhampton and Icetown (in either order), which isn't possible as it's already known that Icetown had (3, 0) and (2, 0) wins.

Hence Frostville lost (0, 4) to Glacierhampton and won (2, 1) against Coldbury.

As Coldbury didn't score any goals against Icetown, they scored three goals against Glacierhampton, and Glacierhampton must have scored 1 goal in that match, as it's already known that Icetown had a (3, 0) win.

Hence Icetown's (3, 0) win was against Glacierhampton and so Icetown's (2, 0) win was against Coldbury.
 
Dec 2019
52
1
ok
You were correct that Icetown had a (0, 1) loss, a (2, 0) win and a (3, 0) win.

You were also correct that as Frostville had a winning score of (1, 0), this was for their match with Icetown, and their remaining scores were (2, 1) and (0, 4).

If Frostville lost (0, 4) to Coldbury, Coldbury's losses were (0, 2) and (0, 3) to Glacierhampton and Icetown (in either order), which isn't possible as it's already known that Icetown had (3, 0) and (2, 0) wins.

Hence Frostville lost (0, 4) to Glacierhampton and won (2, 1) against Coldbury.

As Coldbury didn't score any goals against Icetown, they scored three goals against Glacierhampton, and Glacierhampton must have scored 1 goal in that match, as it's already known that Icetown had a (3, 0) win.

Hence Icetown's (3, 0) win was against Glacierhampton and so Icetown's (2, 0) win was against Coldbury.
Ah, thank you so much! You're always helping me which I admire. Keep doing you!!