English

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 nn 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 n=3n =3. 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}
}
R2 v1 2026-06-28T13:36:07.152Z