### Abstract

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 language | English |
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Article number | R47 |

Journal | Electronic Journal of Combinatorics |

Volume | 14 |

Issue number | 1 R |

DOIs | |

State | Published - 28 Jun 2007 |

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## Cite this

Liao, Y. J., Shieh, M-Z., & Tsai, S-C. (2007). Arranging numbers on circles to reach maximum total variations.

*Electronic Journal of Combinatorics*,*14*(1 R), [R47]. https://doi.org/10.37236/965