September 2018 - Math Problem

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?

 Number seven in small circle surrounded by number three in larger circle

 

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?

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