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Problem of the Week
Problem C and Solution
What’s the Score?


In gym class, the yellow team and the blue team played soccer. Ali doesn’t remember the final score of the game, but she does remember the following.

Determine all the possible final scores and the different ways each score could have been obtained.


In order to win, the blue team must have scored more goals than the yellow team. Since there were six goals scored in total, the only possibilities for the final scores are \(4-2\), \(5-1\), or \(6-0\) for the blue team.

Next we need to check which of these scores are possible, given that neither team scored more than two goals in a row at any point in the game.