A group of prisoners are given a chance to escape. They are given a room with a light bulb that is initially off. Each day, a prisoner is randomly selected to enter the room. While in the room, the prisoner can turn the light bulb on or off. The prisoners can communicate with each other before the game starts, but after that, the only way they can communicate is through the light bulb. How can the prisoners figure out when everyone has been to the room at least once?
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