98. DARTS

Darts is an excellent game – especially if you are in an English pub! The circular board has the numbers 1 to 20 arranged clockwise from the top in the order 20, 1, 18, 4, 13, 6, 10, 15, 2, 17, 3, 19, 7, 16, 8, 11, 14, 9, 12, 5, (20). Other orders are possible; how many, assuming 20 lies at the top? What factors influenced the given arrangement of the numbers? The outer ring scores double the sector score, the central ring triple. The central annulus scores 25, and the central disk 50. What is the highest score obtainable using three darts? What scores are possible using three darts? For any given score, how many ways can it be obtained? There is lots of mathematics and arithmetic here!