Back to Logic Problems
Prisoners and the Light Switch
This Hard puzzle in the “logic” category rewards careful reading and step-by-step reasoning. Use the hint if you are stuck, then compare your approach with the explained answer.
There are 100 prisoners, each held in isolation.
Every day, one prisoner is chosen at random and taken to a central room.
In the room there is a single light switch, which is initially off.
The prisoner may inspect the switch and either change it or leave it as it is.
The prisoners may agree on a strategy beforehand, but after that they may not communicate.
At any time, a prisoner may declare: “Every prisoner has visited the room at least once.”
If the declaration is correct, they all go free. If it is wrong, they all die.
Can they guarantee eventual success?
Preparing…