One hundred people cannot communicate with each other. Their only link to the outside is a light bulb that they can find on or off. The difficulty is that no one knows what state they are in when they start.
The light-bulb room
Riddle statement
There are 100 prisoners. Before you start, you can agree on a strategy. Then, each day, the guard chooses one and takes him to a room with a light bulb, which can be on or off. The prisoners do not know the initial state of the light bulb.
Each prisoner can enter many times. On each visit you can leave the bulb as it is or change its status. When leaving, you cannot communicate with others.
At any time, anyone can declare: “We have all been through the room at least once.” If he is right, everyone is free; If you make a mistake, everyone dies.
What strategy allows you to declare with certainty that everyone has passed through the room?