Prisoners, Rooms, and Lightswitches

by   Daniel M. Kane, et al.

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.


page 1

page 2

page 3

page 4


Localization of Sound Sources in a Room with One Microphone

Estimation of the location of sound sources is usually done using microp...

Quasilinear Rental Harmony

Rental Harmony is the problem of assigning rooms in a rented house to te...

Configuring Multiple Instances with Multi-Configuration

Configuration is a successful application area of Artificial Intelligenc...

God Save the Queen

Queen Daniela of Sardinia is asleep at the center of a round room at the...

Combinatorial Communication in the Locker Room

The reader may be familiar with various problems involving prisoners and...

Please sign up or login with your details

Forgot password? Click here to reset