Question

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. what's the score There were six goals scored in total. Neither team scored more than two goals in a row at any point in the game. Determine all the possible final scores and the different ways each score could have been obtained. The blue team won the game.​

Answer 1

Possible final scores could be 4-2, 3-2, or 3-1 in favor of the blue team. The sequences of goals must comply with the condition that neither team scored more than two goals in a row.

Step-by-step explanation:

Given the conditions that there were six goals scored in total and neither team scored more than two goals in a row, we can determine the possible final scores and the sequences in which these scores could have been obtained. Since the blue team won, we can rule out a tie or a score where the yellow team has more goals.

• The possible final scores could be 4-2, 3-2, or 3-1 in favor of the blue team.
• For a 4-2 final score, the sequence of goals could be B-B-Y-B-Y-B, B-Y-B-B-Y-B, or any other variation that does not have more than two consecutive goals by the same team.
• For a 3-2 final score, sequences could be B-Y-B-Y-B, Y-B-Y-B-B, etc.
• For a 3-1 final score, possible sequences are B-Y-B-B, Y-B-B-B, B-B-Y-B, and so on.

In all these sequences, 'B' stands for a goal by the blue team, and 'Y' stands for a goal by the yellow team.

Answer 2

Step-by-step explanation:

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