Nov 2, 2011 #1 J Jorge Member Joined May 12, 2008 Messages 181 Reaction score 0 Points 16 Suppose 3 and 8 are the only individual scores in a game of darts. So it is possible to earn scores of 6, 9, 11, 12, 15, 16, etc. Which scores are impossible to earn? How many different scores are impossible to earn?
Suppose 3 and 8 are the only individual scores in a game of darts. So it is possible to earn scores of 6, 9, 11, 12, 15, 16, etc. Which scores are impossible to earn? How many different scores are impossible to earn?
Nov 2, 2011 #2 K kiwiJOEY New member Joined Nov 2, 2011 Messages 1 Reaction score 0 Points 1 In general, if two numbers a and b have no common factors, the highest number that cannot be scored is ab - a - b. In this case it will be 3*8 - 3 - 8 = 13. All numbers above 13 can be scored. now let's list those that can't: 1, 2, 4, 5, 7, 10, 13 ... seven scores.
In general, if two numbers a and b have no common factors, the highest number that cannot be scored is ab - a - b. In this case it will be 3*8 - 3 - 8 = 13. All numbers above 13 can be scored. now let's list those that can't: 1, 2, 4, 5, 7, 10, 13 ... seven scores.