The arrangement of the numbers around the circumference of a standard dart board is as shown below
20 1 18 4 13 6 10 15 2 17 3 19 7 16 8 11 14 9 12 5
Oddly enough, no one seems to know for sure how this particular arrangement was selected. ... it's clear that the numbers are ordered to mix the large and small together, and possibly to separate numerically close values as far as possible (e.g., 20 is far from 19), no one seems to know of any simple criterion that uniquely singles out this particular arrangement as the best possible in any quantitative sense.
This appears to be an unsolved problem. How did the inventor of the standard dartboard come up with the order of the numbers in such a way as to minimise scores that are produced by inaccurate throws?
Can anyone see a pattern or was it just trial and error?
Given that computers weren't available then (pre 1900), can anyone suggest a pencil and paper method that produces a near-optimum result (and specifically this result) in a reasonable time?