You throw a dart at the board below repeatedly. Each time you hit the board, you add either 7 or 3 to your score depending on which part you hit. What is the largest score that you can not get in this game? How do you know?
Solution:
Score 3 Hits 3
Score 6 Hits 3,3
Score 7 Hits 7
Score 9 Hits 3,3,3
Score 10 Hits 3,7
Score 12 Hits 3,3,3,3
Score 13 Hits 3,3,7
Score 14 Hits 7,7
Score 15 Hits Answer for 12 and 3
Score 16 Hits Answer for 13 and 3
Score 17 Hits Answer for 14 and 3
Score 18 Hits Answer for 12 and 3 and 3
We can keep adding 3 to the answers for 12, 13, and 14 to get all of the numbers greater than 14. This means that the highest score that we can not get is 11.
What would be the highest score that you could not get if there were three sections on the dart board with the numbers 5, 7 and 9?
What would be the highest score that you could not get if there were two sections on the dart board with the numbers 2 and 4?