Can you solve it? Two dead at the drink-off – a brilliant new lateral thinking puzzle | Mathematics

Today’s puzzle is attributed to Michael Rabin, the legendary computer scientist, who in the late 1980s posted it on an electronic bulletin board at Carnegie Mellon University.

It was recently highlighted by a puzzle enthusiast who believes it deserves to be better known. I agree – it’s an all-time classic.

There are no tricks, but you have to think laterally. The solution relies on basic game theory: both participants act in their own self-interest based on what they think the other will do.

Two deaths from drinking

In a distant land, the following facts are true and known to all:

1) A person who ingests a poison will die within an hour, UNLESS they ingest a more powerful poison, which acts as an antidote and restores full health.

2) Smith and Jones are the only poison manufacturers.

3) Everyone 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 if Smith or Jones make the more powerful poison. One day, the queen decides to find out. She summons Smith and Jones to her palace and says:

“In a week, you will both return here. Bring a vial of your own poison. There will be a ceremony. First, you will both take a sip from the other’s vial. Then, you will both take a sip from your own vials. You will then be monitored for an hour.

“It is in your own interest 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 can’t cheat.”

Smith and Jones leave, both very disturbed. They don’t want to die and none of them are sure they have the most powerful poison. Neither has any way of accessing the other’s poisons. They rack their brains all week trying to think of the best way to ensure their own survival. The appointed time arrives. The ceremony takes place exactly as planned by the Queen. Smith and Jones drink each other’s bottles, then their own. They are carefully monitored for an hour.

To everyone’s surprise, Smith and Jones collapse and die! The Royal Coroner confirms that both died of poisoning.

What happened?

I’ll be back at 5pm in the UK with the solution.

UPDATE: The solution can be read here.

In the meantime, NO SPOILERS. Instead, share your favorite “what happened?” » type of lateral thinking puzzle.

Thanks to mathematician Timothy Chow of the Center for Communications Research in Princeton, New Jersey. Timothy first saw the puzzle in the 1980s and always kept it in mind. He recently published an article on this subject in Mathematics review (paywall), which inspired this column. I have slightly rewritten the original wording of the puzzle.

I’ve been putting up a puzzle here every other Monday since 2015. I’m always looking for great puzzles. If you want to suggest one, send me an email.