Arranging numbers on circles to reach maximum total variations

Ying Jie Liao*, Min-Zheng Shieh, Shi-Chun Tsai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The dartboard problem is to arrange n numbers on a circle to obtain maximum risk, which is the sum of the q-th power of the absolute differences of adjacent numbers, for q ≥ 1. Curtis showed that the dartboard problem admits a greedy algorithm. We generalize the dartboard problem by considering more circles and the goal is to arrange kn number on k circles to obtain the maximum risk. In this paper, we characterize an optimal arrangement for k = 2 and show that the generalized dartboard problem also admits a greedy algorithm.

Original languageEnglish
Article numberR47
JournalElectronic Journal of Combinatorics
Issue number1 R
StatePublished - 28 Jun 2007

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