In 2014, Howard returned from his football game later than normal and Trudy, his Mom, was concerned. She asked what position he played, and he said he was a lineman. She asked what team they played and he said the Bears. She asked if anything strange had happened, and he said no. She asked what the score was and he said their team won, 14-1. Satisfied, Trudy sent Howard up to bed. The next morning Trudy told her husband Mick about her conversation with Howard. Mick’s face turned red and he stormed up to Howard’s room.
Mick knew Howard was lying about being at the football game because in American football it’s impossible to score just 1 point (before the 2015 one-point safety rule). A score of 2 is the lowest possible score (awarded for a safety). In fact, 1 is the only impossible score in football. You can score 2 points for a safety, 3 points for a field goal and 6 points for a touchdown, with an extra point for the field goal. You also have the option to go for another touchdown for a 2-point conversion. With 2, 3, 6 and 7 you can generate any other number except for 1.
For example, here are ways a team could score from 2 to 10 points.
2 = safety
3 = field goal
4 = 2 + 2
5 = 3 + 2
6 = touchdown
7 = touchdown and extra point attempt
8 = touchdown and two point conversion
9 = touchdown and field goal
10 = touchdown, extra point attempt and field goal
1 lb = A
2 lbs + A = B
3 lbs = B
4 lbs = A + B
5 lbs + A + B = C
6 lbs + B = C
7 lbs + B = A + C
8 lbs + A = C
9 lbs = C
10 lbs = A + C
11 lbs + A = B + C
12 lbs = B + C
13 lbs = A + B + C
14 lbs + B = D
15 lbs + B = A + D
16 lbs + A = D
17 lbs = D
18 lbs = A + D
19 lbs + A = B + D
20 lbs = B + D
21 lbs = A + B + D
22 lbs + A + B = C + D
23 lbs + B = C + D
24 lbs + B = A + C + D
25 lbs + A = C + D
26 lbs = C + D
27 lbs = A + C + D
28 lbs + A = B + C + D
29 lbs = B + C + D
30 lbs = A + B + C + D