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A proof of the
optimal leapfrogging conjecture
Sam K. Miller and Arthur T. Benjamin |
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Vol. 18 (2025), No. 1, 105–122
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Abstract |
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Consider a collection of checkers that move on the integer lattice by shifting or jumping. It has been shown that a configuration of pieces can translate itself at a speed of at most 1, and this can only be achieved with a collection of 1, 2 or 4 checkers. We prove the conjecture that with any other number of checkers, the fastest obtainable speed is . |
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Keywords
leapfrogging, games on grid
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Mathematical Subject Classification
Primary: 00A08
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Milestones
Received: 15 April 2023
Revised: 15 August 2023
Accepted: 30 August 2023
Published: 24 January 2025
Communicated by Glenn Hurlbert
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Authors |
| Sam K. Miller | |
| Department of Mathematics University of California Santa Cruz Santa Cruz, CA United States |
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| Arthur T. Benjamin | |
| Department of Mathematics Harvey Mudd College Claremont, CA United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
