Earlier today I set you the following puzzle. Here it is again with the solution.
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?
Solution
They both died because both Smith and Jones drank a weak poison just before arriving at the ceremony, and, instead of bringing a strong poison as requested, brought water. Each drank the other’s water, then drank their own water, and then died of their own poison.
But why did they do this?
Smith was hoping that Jones would not think of the same trick and would, as requested, bring a strong poison to the showdown. That way, Jones’ strong poison would cure Smith of Smith’s own weak poison, and Smith would live, whereas Jones would die from drinking his own poison.
(There would remain the risk that the Queen would discover the attempt to circumvent the rules, but this risk could be mitigated by Smith drinking every last drop of water.)
Yet Jones thought similarly, and so both died.
This puzzle was conceived by Michael Rabin in the 1980s and recently brought to light by the mathematician Timothy Chow, of the Centre for Communications Research in Princeton, New Jersey. To read more, please read his article on it in Mathematics Magazine (paywall). 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.
