Solving the City Soccer Tournament Puzzle: Group A Results

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SUMMARY

The city soccer tournament puzzle for Group A has been solved, revealing the match scores based on the teams' goals and points. The final standings were: Naranja with 7 points, Bleu with 6 points, Midori with 3 points, and Gelb with 1 point. The match results are as follows: Naranja defeated Bleu 2-1, Naranja beat Midori 1-0, Naranja and Gelb tied 1-1, Bleu triumphed over Midori 2-0, Bleu won against Gelb 2-0, and Midori defeated Gelb 1-0. This analysis confirms the accuracy of the points distribution based on the match outcomes.

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mathgeek7365
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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?
 
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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]
 

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