Here is another riddle. This one is tough. It took me about 20 minutes to figure it out the first time after a shitload of intense thinking.
Again, some of you might remember this riddle from the old forum. Please don't spoil it for everybody right away.
So here goes.
There is a prison with 100 prisoners. Each one resides in a completely isolated cell. The warden is sick of his job and makes the prisoners an offer.
There is a room with 2 switches. The switches have only two states (OFF and ON) which makes a total of 4 possible states (OFF + OFF, OFF + ON, ON + OFF, ON + ON). The switches themselves don't do anything. A guard will completely randomly take a prisoner out of his cell and let him change the state of one of the switches. The prisoner MUST change the state. As all prisoners are isolated, nobody knows how many prisoners were out already and which ones were out. To make things harder, nobody knows the initial states of the switches. Each prisoner can be taken out more than once.
Now, the warden's offer is to let all prisoners go if they can tell him when all 100 prisoners were out changing switches at least once. Any prisoner can do that and it's alright if a prisoner was out more than once. It's only important that each one was out at least once. The warden allows the prisoners to have a conversation before the beginning of this procedure to make an agreement about what they are going to do. Remember, there is no way to communicate for them otherwise after the initial agreement.
How do they ensure that they will be released with a chance of 100%? What do they need to do with the switches? Sure, they could just guess or wait really long, but that's not going to get them out for 100%.
Assume that each prisoner will be out at least once in finite time. That means it will not happen that one of the prisoners will never get out to change the switches.
Remember that they don't have to tell the guard everybody was out at least once immediately after everybody was out at least once.