A dart board is designed to have two scoring areas, as shown. If an unlimited number of darts is allowed, what is the largest finite score that cannot be attained?

I couldn't draw the two circles so I'll explain. If the dart landed on the outer circle if would count for 7 points and the inner circle would count for 15.

I see that I will be able to get all the multiples of 7

7 14 21 28 35 42

and then if i get a 15 and then all 7 i can get all the

15 22 29 36 43

and I get 7 and all 15..

7 22 37 52...

and I can't see how to get the largest finite score that can't be attained.

I tried other combinations also. Maybe i am doing it too randomly.

Could you please explain the logic of this problem step by step.

Thanks.

Vicky.