In regular American football, teams can score 2 points for a safety and 3 points for a field goal. In the right combinations, any point total > 1 is possible. But in this imaginary new-fangled who-cares-about-defense version of American football, teams can only score 3 points for a field goal or 7 points for a touchdown (extra points are automatic). No other scoring plays exist.
What's the largest score that is impossible for a team to get?
Ready for the answer?
Did you know this actually wasn't a football question at all? This is a problem in mathematics called the Frobenius coin problem (follow the link to geek out!).
You can see how it's related to coins; what amount of money is impossible to make given certain denominations? In this case, imagine a country with only two denominations: $3 and $7. What is the largest amount of money that is impossible to have?
Here, the answer is 11. There is no combination of 3 and 7 that can make 11.
How do we know we can score any number of points 12 or higher?
- 12 = 3 + 3 +3 +3
- 13 = 7 + 3 + 3
- 14 = 7 + 7