Nov 2, 2011 #1 J Jorge Member May 12, 2008 181 0 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 Nov 2, 2011 1 0 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.