Late Friday Puzzler -- 100 Prisoners

Alex Y
100 prisoners with life sentences are presented with a challenge that will grant them freedom if they succeed, but death if they fail.

There is a room in the prison with a light and a switch that controls the light. The prisoners are told that light is off at the beginning of this challenge.

The jailer has a bowl with chips numbered 1-100, which he will use every 15 minutes to choose a prisoner at random (replacing the chip after choosing the prisoner). The prisoner will go into the room and may turn the light on, turn it off, or leave its state unchanged, and then return to his cell or make a claim for freedom. If a prisoner correctly tells the jailer that all the prisoners have been chosen to go into the room, then they all go free. If he makes that claim but some prisoner(s) has not been selected yet to go into the room, they are all executed.

The prisoners are given some time to determine what strategy they want to use, but once the selections start, they are not able to communicate with each other, or see whether the light is on or off when prisoners enter or exit the room.

What strategy should they adopt to assure, or maximize the chance of, their freedom?

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