Abstract:
This note considers possible arrangements of the sectors of a generalised dartboard.
The sum of the pth powers of the absolute differences of the numbers on adjacent
sectors is introduced as a penalty cost function and a string reversal algorithm is
used to determine all arrangements that maximise the penalty, for any p >_1. The
maximum value of the penalty function for p = 1 is well known in the literature,
and has been previously stated without proof for p = 2. We determine it also for
p = 3 and p = 4.
