MHB Solving the City Soccer Tournament Puzzle: Group A Results

[mathgeek7365]

My daughter needs my help, and I am stumped. Here is the problem:

In the first round of the city soccer tournament, the teams in group A finished as follows:
Team------>Goals For------>Goals Against----->Points
Naranja---> 4--------------->2-------------------->7
Bleu------> 5---------------->2-------------------->6
Midori---->1----------------->3-------------------->3
Gelb------>1----------------->4-------------------->1

A victory earns three points, a tie one point, and a loss no points. Each team played the other three once. What were the scores of all the matches?

 

[MarkFL]

I really could only find the solution by trial and error:

[TABLE="class: grid, width: 400, align: left"]
[TR]
[TD]Team[/TD]
[TD]Score[/TD]
[TD]Team[/TD]
[TD]Score[/TD]
[/TR]
[TR]
[TD]Naranja[/TD]
[TD]2
[/TD]
[TD]Bleu[/TD]
[TD]1
[/TD]
[/TR]
[TR]
[TD]Naranja[/TD]
[TD]1
[/TD]
[TD]Midori[/TD]
[TD]0
[/TD]
[/TR]
[TR]
[TD]Naranja[/TD]
[TD]1[/TD]
[TD]Gelb[/TD]
[TD]1[/TD]
[/TR]
[TR]
[TD]Bleu[/TD]
[TD]2
[/TD]
[TD]Midori[/TD]
[TD]0[/TD]
[/TR]
[TR]
[TD]Bleu[/TD]
[TD]2[/TD]
[TD]Gelb[/TD]
[TD]0[/TD]
[/TR]
[TR]
[TD]Midori[/TD]
[TD]1[/TD]
[TD]Gelb[/TD]
[TD]0[/TD]
[/TR]
[/TABLE]