Qiaochu's recent question reminded me of something I've wanted to know for some time, which is the name of the person who first came up with puzzle below. I first heard about it around 1990 at Carnegie Mellon and was told that someone called "Michael Rabin" was the inventor, but I have never been able to confirm that. (I once sent an email inquiry to the one Michael Rabin I knew about but never received a reply.) Can anyone provide any more information?
EDIT: Some people asked what this has to do with mathematical research. It turns out that in addition to the solution that was clearly intended, there are additional solutions that in some sense build on the intended solution. Analyzing how these solutions interact leads to a fairly subtle game-theoretic problem. I have thought about writing a paper on the subject, though given that this has been on my back burner for such a long time, I don't know when I'll actually get around to it...
There is a world in which the inhabitants have a strange physiology. If a healthy person ingests a poison, he will die within an hour unless he ingests a stronger poison, in which case he becomes healthy again. The poisons in this world are strictly linearly ordered in strength. Moreover there are two kinds of poisons: magical and medical, which are dispensed by the Royal Magician and the Royal Physician respectively. No magical poison has the same strength as a medical poison. All of these facts are common knowledge.
The King decides that he wants to find the strongest poison in the land, because it will not only be very useful for eliminating enemies but will also act as an antidote against any other poison. So he calls in the Royal Magician and the Royal Physician and says, "I want each of you to return here to my royal chambers at noon one week from now. Bring a vial of your strongest poison. To give you incentive to bring your strongest poison, you must do the following: each of you must drink from the other's vial first and then drink from your own vial. I will have trained observers present to make sure that you cannot cheat. Then you will be watched for one hour, during which you may not ingest any substances. The person who has the stronger poison will of course survive and the other will die. This is unfortunate but I have decided that it is worth it, in the interests of national security. If I detect any attempt to circumvent these rules you will both be executed. You may go now, but you must return at the specified time."
The Royal Physician and the Royal Magician go off, both very disturbed, because neither wants to die. Each has had some experience with the other's poisons and knows that some of them are quite potent. Neither of them is fully confident of having the strongest poison. Nor does either have any way of getting access to the other's poisons. They rack their brains all week trying to think how they can best ensure their own survival.
The appointed time rolls around and the two Royal Servants return. They follow the specified protocol exactly, and are watched carefully for one hour. To everyone's astonishment, both Royal Servants keel over and die within the hour. The Royal Coroner confirms that both died of poisoning.
- Explain what happened in the way the person who originally devised the puzzle intended.
- Cook the puzzle by finding three alternative explanations.
The answers to the puzzle as stated here (though not the game-theoretic problem that it leads to) may be found in this rec.puzzles post that I made back in 1992.