Following on from BUFD version of the Bowling Game (given that we've
figured out the solution as far as #3) a language with pattern
matching and list functions would allow a recursive solution (compare
to #4) like this:

   Start = score [0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 10,
5,3] 0 0

   score pins total 10 = total

   score [x,y] total frame = total + x + y

   score [x,y,z:rest] total frame
      | x == 10    = score [y,z:rest] (total+x+y+z) (frame+1)
      | x+y == 10  = score [z:rest] (total+x+y+z) (frame+1)
      | otherwise  = score [z:rest] (total+x+y) (frame+1)

To explain:
- if we've done 10 frames we're finished
- if there are only 2 items we're finished (main clause needs 3 items
to match)
- 3 rules for calculating the score

best wishes, Isaac