Puzzles
100 prisoners, one lightbulb, and no way to talk to each other
A warden puts 100 prisoners in isolation. Each day he picks one at random and sends them alone into a room with a single lightbulb, which they may switch on or off. Any prisoner may declare 'everyone has visited this room' — if right, all go free; if wrong, all are executed. They can agree a strategy beforehand, but never communicate again. What strategy guarantees freedom?
Reveal the answer
Appoint one prisoner as the sole 'counter'. Every other prisoner turns the light on the first time they find it off (and never touches it again after that). The counter turns it off each time they find it on and keeps a tally; once their count reaches 99, everyone has visited, so they make the declaration. It takes a while, but it's guaranteed to work.