"Take a look around you. I am going to lock up all 100 of you scum. Unless you can solve my puzzle, none of you will ever see the light of day, and none of you will ever see each other, ever again.
I am going to throw you all into cells. Every day, right after supper, I will randomly pick a prisoner, and take them to a room. In that room there is one lightbulb and one switch.
The only thing you will be permitted to do in the room is look at the lightbulb, and flip the switch that turns the lightbulb on and off if you want to.
Then you will be removed from the room, and returned to your cell, unless you claim that every single prisoner has been in the room.
If you make this claim, and you are right, you are all free to go.
If you make this claim, and you are wrong, you will all be killed.
Enjoy your last hour of contact with each other, scumbags. You get to spend the next hour thinking up the best plan your feeble minds are capable of."
Can the prisoners escape?
(Note: This is a reasonably famous puzzle. Many people will have the answer at their fingertips. I advise you to try solving it before reading the spoilers!)
1. The prisoners cannot keep time. They cannot tell how many days it has been since the start of the test, or how many days it has been since they last where in the room.
2. The prisoners are robots. They can all follow the same algorithm, but they are not allowed to have a distinct prisoner before hand.