There is a prison with a twisted and sadistic warden. The prison holds one hundred prisoners, each in separate cells. Each cell is sealed off from the others, soundproof and windowless. There is a lobby in the prison with a lightbulb in it.
Each day, the warden will choose one of the prisoners at random (even if they’ve been chosen previously) and take them to the lobby. The prisoner will have the choice to flip the lightbulb switch if they want. The lightbulb starts in the “off” position.
When a prisoner is brought to the lobby, they also have the option of saying “All other prisoners have been brought to the lobby”. If they do so and it’s true, all the prisoners will be freed. IF they say that and it’s not true, all the prisoners will be executed.
Before the first day this begins, the prisoners are allowed to get together to discuss what they will do. What strategy could they use to save themselves?