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March 24, 2017

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A certain football league has the following scoring system:

- each field goal counts for 5 points
- each touchdown counts for 3 points

The only way to score points is with some combination of field goals
and touchdowns.

They have noticed that not every score is possible in this league
(for example 1, 2, 4...); in fact they think that they know the
highest score that is impossible to make. I have figured out that this
is 7 points, but I would like to know why. How can I prove that this
score is impossible and that all higher scores are possible?

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