November 5, 2013
Problem of the Week
for Tuesday, November 5, 2013
Three prisoners are offered an opportunity. They will be brought at random and one at a time into a room that contains a simple light switch and a working light. Any prisoner my be brought into this room multiple times, even multiple times in succession. If any one of the prisoners is able at any time to correctly deduce that all three of them have been brought into this room, the prisoners will be set free. If the deduction is incorrect, they will be executed. If they are allowed to meet and confer together before the random procedure begins, what plan will ensure their release and not run the risk of execution? Assume that the light is on at the beginning and that only the prisoners are allowed to flip the light switch.