5 (five)
The numbers in each column give the distinct number of ways to score that number of points in a football game.
There are three main ways to score in football, by touchdown, field goal, or safety.
A safety is worth two points.
A field goal is worth three points.
A touchdown is worth six points. After scoring a touchdown, a team has the option of kicking for another extra point, or trying to drive back into the end zone for two points (called a two-point conversion). Of course, either of these attempts could fail and the team would score only the six points for the touchdown.
Given that, the possible ways to score are:
- Cannot be done
- One safety (2)
- One field goal (3)
- Two safeties (2+2)
- One safety and one field goal (2+3)
- One touchdown (6)
Two field goals (3+3)
Three safeties (2+2+2)
- A touchdown with the extra point (7)
A field goal and two safeties (3+2+2)
- Four safeties (2+2+2+2)
Two field goals and a safety (3+3+2)
A touchdown and a safety (6+2)
A touchdown with a two-point conversion (8)
- Three field goals (3+3+3)
A touchdown and a field goal (6+3)
A touchdown with the extra point and a safety (7+2)
One field goal and three safeties (3+2+2+2)
- A touchdown with the extra point and a field goal (7+3)
Five safeties (2+2+2+2+2)
Two field goals and two safeties (3+3+2+2)
A touchdown and two safeties (6+2+2)
A touchdown with a two-point conversion and a safety
(8+2)
So, there are five different ways to score ten points in a football game.
Another way to arrive at the same analysis, without having to know anything about any sport, would simply be to say that the number in the second row is the number of ways you can generate the number in the first row by adding the numbers 2, 3, 6, 7, and 8. |
