I came across this nice little puzzle that I got from the Quora website from someone named Alejandro Jenkins who said that he cannot recall where he first heard or read about it. In its essentials it is easy to state and understand even though, as seems to be the tradition with such puzzles, a story is constructed around it.
The two leading mathematicians in the kingdom, Alice and Bob, have run afoul of their tyrannical king. Rather than behead them outright, the king decides to prolong their misery by locking them in separate dungeons, so that any communication between them is impossible.
Each morning, a guard is to enter the corresponding dungeon and toss a coin so that the prisoner in that dungeon can see the outcome. Then the prisoner will be asked to guess the outcome of the coin toss in the other dungeon (i.e., Alice has to guess the outcome of the toss witnessed by Bob, and Bob has to guess the outcome of the toss witnessed by Alice). If at least one of the two prisoners guesses correctly, they will live to see another day. Otherwise they will be put to death forthwith.
It would seem that the mathematicians are doomed. But as they are being led away in chains Alice and Bob manage to confer for a brief moment and they agree on a strategy that will delay their execution indefinitely. What is the strategy?
What I like about this puzzle is that there is no trickery involved, no hidden meanings and the like. It is a straightforward logic puzzle. Jenkins provides the solution but for some reason, I cannot deep link to it and so will wait a day to let people discuss it in the comments if they so choose and then post the solution in the comments.