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Today’s puzzle is credited to Michael Rabin, the legendary computer scientist, who in the late 1980s posted it to an electronic bulletin board at Carnegie Mellon University.
It has recently been brought to light by a puzzle enthusiast who thinks it deserves to be better known. I agree – it’s an all time classic.
There are no tricks, but you need to think laterally. The solution involves basic game theory – the two participants are acting in their own interests based on what they think the other one will do.
Two dead at the drink-off
In a far away land, the following facts are true and known to everyone:
1) A person who ingests a poison will die within the hour UNLESS that person ingests a stronger poison, which acts as an antidote and restores complete health.
2) Smith and Jones are the only manufacturers of poison.
3) Each makes several types of poison.
4) All poisons have different strengths.
5) Smith and Jones do not have access to each other’s poisons.
No one knows whether Smith or Jones makes the strongest poison. One day the Queen decides to find out. She summons Smith and Jones to her palace and says:
“In one week from now, you will both return here. Bring a vial of your own poison. There will be a ceremony. First, both of you will take a swig from the other one’s vial. Next, you will both take a swig from your own vials. You will then be watched for one hour.
“It is in your own interests to bring your strongest poison. The person who brings the strongest poison will obviously survive. The other person will clearly die. There will be trained observers to make sure you cannot cheat.”
Smith and Jones leave, both very disturbed. They do not want to die, and neither is confident of having the strongest poison. Nor does either have any way of getting access to the other’s poisons. They wrack their brains all week trying to think how they can best ensure their own survival. The appointed time arrives. The ceremony takes place exactly as planned by the Queen. Smith and Jones swig each other’s vials and then their own. They are watched carefully for one hour.
To everyone’s astonishment, both Smith and Jones keel over and die! The Royal Coroner confirms that both died of poisoning.
What happened?
I’ll be back at 5pm UK with the solution.
Meanwhile, NO SPOILERS. Instead please share your favourite “what happened?” type of lateral thinking puzzle.
Thanks to the mathematician Timothy Chow, of the Centre for Communications Research in Princeton, New Jersey. Timothy first saw the puzzle in the 1980s and always kept it in the back of his mind. Recently he published an article on it in Mathematics Magazine (paywall), which was the inspiration for this column. I’ve slightly rewritten the original wording of the puzzle.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
