In a football game, a touchdown with an extra point is worth 7 points and a field goal is worth 3 points. Suppose that in a game the only scoring done by teams are touchdowns
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Sure, I'd be happy to help!
In the given scenario, we know that teams can only score touchdowns, and we need to find the possible scores that can be achieved.
To start, we know that a touchdown with an extra point is worth 7 points. The extra point is essentially 1 additional point after a touchdown is scored.
So, if we consider all the possible combinations of touchdowns and extra points, we can have the following:
1 touchdown with 0 extra points: This would give us a score of 7 points.
1 touchdown with 1 extra point: This would give us a score of 8 points.
1 touchdown with 2 extra points: This would give us a score of 9 points.
1 touchdown with 3 extra points: This would give us a score of 10 points.
1 touchdown with 4 extra points: This would give us a score of 11 points.
...
As we can see, the score increases by 1 point each time an additional extra point is scored after a touchdown.
So, if the only scoring done in the game is touchdowns, the possible scores can be any odd number starting from 7 (since touchdowns are worth an odd number of points).