After enjoying the various problems already posted here, I thought I'd share one I found quite interesting:
You have 50 people taken prisoner. They are gathered together, and told the following rules:
Once they have been told the rules, they will have time to discuss a plan amongst themselves. After they have finished, they will each be placed in a separate cell, and unable to communicate with each other.
At unspecified (and unpredictable) time intervals, one of them will be selected (independent of prior selections), and led to a room, in which there is a single switch, which can be set to 0 or 1. They are not told what position it will start in. Once in the room, the can either flick the switch or not. Either way, they are then led back to their cell. This process then repeats.
At any point, if any of them knows for certain that all of them have been in the room at least once, they can say so, and all of them will go free. They must be able to explain why they know for certain. Simply waiting a long time and hoping that everyone has been through isn't good enough.
You can assume they're all perfectly logical, trying to escape, and will act according to the plan.
I think that's it - just say if there's anything I've missed, or anything you want clarification on.