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Publications
  • 2021
  • Article
  • Electronic Journal of Combinatorics

Prisoners, Rooms, and Lightswitches

By: Daniel M. Kane and Scott Duke Kominers
  • Format:Electronic
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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.

Keywords

Mathematical Methods

Citation

Kane, Daniel M., and Scott Duke Kominers. "Prisoners, Rooms, and Lightswitches." Electronic Journal of Combinatorics 28, no. 1 (2021).
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About The Author

Scott Duke Kominers

Entrepreneurial Management
→More Publications

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More from the Authors
  • Collusion in Brokered Markets By: John William Hatfield, Scott Duke Kominers and Richard Lowery
  • Harvard Students Should Ignore Calls to Boycott Israel Trek By: Jesse M. Fried, Paul A. Gompers, Scott Kominers and Mark C. Poznansky
  • O2X: Optimizing to the X By: Scott Duke Kominers, Thomas Jennings and Maisie Wiltshire-Gordon
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