Variations on Keeler's Theorem
Combinatorics
2023-12-01 v1
Abstract
The 2010 Futurama episode The Prisoner of Benda features a mind swapping machine that swaps the minds of two people at a time with the restriction that the same pair of people cannot use the machine more than once. We show that if a machine swaps people cyclically with the condition that the same group of people cannot use the machine again, we can find a way to get everyone back. We prove our solution is optimal for when . We also introduce an infinite variant of the mind swapping machine.
Cite
@article{arxiv.2311.18080,
title = {Variations on Keeler's Theorem},
author = {Alexandra Bartas and Danny Lara and Bruce Leavitt and Ben Vessely},
journal= {arXiv preprint arXiv:2311.18080},
year = {2023}
}