There are 21 prisoners, the guards announce the following.
They will randomly select a prisoner, and bring him into a room.
This will repeat indefinitely, until one prisoner will declare that all of the prisoners have been in the room at least once.
If this is true they are released, if not they are executed.
What do the prisoners do?
I'll change it up a little.
Instead of a clock, say there are 2 light switches in the room.
The light switches are not connected to anything and can either be in the off position or the on position.
Each time a prisoner is brought in he must flip one switch. He can do nothing else.
The prisoners do not know the starting position of the switches and they have no way of knowing which order or how many times they will be brought in to the room.