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- W4287665613 abstract "We examine a new variant of the classic prisoners and lightswitches puzzle: A warden leads his $n$ prisoners in and out of $r$ rooms, one at a time, in some order, with each prisoner eventually visiting every room an arbitrarily large number of times. The rooms are indistinguishable, except that each one has $s$ lightswitches; the prisoners win their freedom if at some point a prisoner can correctly declare that each prisoner has been in every room at least once. What is the minimum number of switches per room, $s$, such that the prisoners can manage this? We show that if the prisoners do not know the switches' starting configuration, then they have no chance of escape -- but if the prisoners do know the starting configuration, then the minimum sufficient $s$ is surprisingly small. The analysis gives rise to a number of puzzling open questions, as well." @default.
- W4287665613 created "2022-07-25" @default.
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- W4287665613 date "2020-09-17" @default.
- W4287665613 modified "2023-09-24" @default.
- W4287665613 title "Prisoners, Rooms, and Lightswitches" @default.
- W4287665613 doi "https://doi.org/10.48550/arxiv.2009.08575" @default.
- W4287665613 hasPublicationYear "2020" @default.
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