The Chicago Bears score 18 points in a football game. In how many different ways can the Bears score these points? Points are scored as follows: a safety is 2 points, a field goal is 3 points, a touchdown is 6 points, and a point after touchdown (PAT) is 1 point (a PAT can't be scored unless a touchdown is scored first).
From here on out, I abbreviated Touchdown as TD, Field Goal as FG, and point after touchdown as PAT. I created a systematic list, beginning with the maximum number of touchdowns scored and then the maximum amount of field goals with 2 touchdowns and so on until I was left with no further solutions. To make it easier for you to read, I just inputted my data into Excel and took a screenshot.
I am wondering if I accidently skipped over a possible way when making my list. Keep in mind, there are NO 2-point conversions after a TD is scored. I also assumed that you could miss a PAT, even though it is unlikely (but, so are some of these solutions below - 9 safeties, really?).
My systematic list:
I got a total of 14 ways.