20 life-sentence prisoners are called into the worden's office one day, and given a proposition.
"Every day, I will select one of you at random and take you into a room. In that room is a single switch, clearly marked on/off. While you are in the room, you can flip the switch or do nothing. Right now, the switch is off.
"You will be allowed to discuss your strategy today, but after that you will return to solitary confinement and will have no other contact with each other.
"At some point in the future, one of you will announce that everyone has been into the room at least once. If that person is correct, you will all be set free. If they are wrong, you will all be killed."
What is their best strategy?