Math CentralQuandaries & Queries


Question from Riaan, a student:

Good day, I would like to know all the possible scores for a set of 5 soccer matches with no more than 5 total goals being scored in any match.
Bearing in mind that there are three outcomes to every match. Win, Lose or Draw.
Could you please help me with this?

Kind regards
South Africa

Hi Riaan,

Let's look at one of the matches. If the teams draw then the scores are 0,0; 1,1; or 2,2.

Suppose the teams are A and B. I want to list the scores in the games that A lost.

If A scored 0 goals then B could score 1, 2, 3, 4, or 5 goals.

If A scored 1 goal then what are the possible number of goals that B could score?

What if A scored 2 goals?

What are the possible scores if B won the match?


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