Dartboard Arrangements

NJ Calkin & HS Wilf
Publication Type:
Journal Article
Electronic Journal of Combinatorics, 2001, 8 (2), pp. 1 - 8
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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.
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