In a certain football league, the only way to score is to kick a eld goal
for 3 points or score a touchdown for 7 points. Thus the scores 1, 4
and 8 are not possible. How many positive scores are not possible?
Choose the correct choice from the following answers:
A) 5
B) 6
C) 9
D) 11
E) infinitely many
One checks directly that the following list of scores up to 14 is the complete list   of obtainable scores up to that point: 3, 6, 7, 9, 10, 12, 13, 14. Now, we have 3 consecutive   scores, namely 12, 13, and 14, which are obtainable, and this implies every score &gt; 14 is   obtainable. To see this, observe that if n is an obtainable score, then so is n + 3 (simply   add another eld goal to whatever it took to get n points); hence, 15 = 12+3, 16 = 13+3,   and 17 = 14+3 are all obtainable and so are 18 = 15+3, 19 = 16+3, 20 = 17+3, and so   on. Therefore, the positive integral scores which are not obtainable are 1, 2, 4, 5, 8, and   11. Thus, the answer is 6   correct answer 6
<result>B</result>
In a certain football league, the only way to score is to kick a eld goal
for 3 points or score a touchdown for 7 points. Thus the scores 1, 4
and 8 are not possible. How many positive scores are not possible?