In football (american, not soccer) if you have possession of the ball you can score 3 points with a field goal, or 6 points with a touchdown, which can be followed by 1 or 2 extra points. Thus, for example, you cannot manage a total score of just 2 points. (As a matter of fact, you
could get this score with a "safety", but let's disregard this unlikely possibility and forget safeties.) What's the maximum unattainable score?
Another question: assuming you could only score field goals for 3 points and touchdowns for 7 points... what would then be the maximum unattainable score?
For the second question, if you could score X and Y points, with X and
Y relatively prime, the maximum unattainable score would be XY-X-Y; in
this case, 21-7-3=11.
Generalizing
