The prisoners and hats puzzle is an induction puzzle (a kind of logic puzzle) that involves reasoning about the actions of other people, drawing in aspects of Game theory sometimes called the hierarchy of beliefs. There are many variations, but the central theme remains the same. Not to be confused with the similar Hat Puzzle.
Other articles related to "prisoners and hats puzzle, prisoners, prisoner, hat":
... It turns out that, if one allows the prisoners to hear the colors called out by the other prisoners, it is possible to guarantee the life of every prisoner except the first, who dies with a 50 ... this information, everyone after him can determine exactly what his own hat color is ... which of the two possible strings the first person saw, and thus he can determine his own hat color ...
Famous quotes containing the words puzzle, prisoners and/or hats:
“Waiting for the race to become official, he began to feel as if he had as much effect on the final outcome of the operation as a single piece of a jumbo jigsaw puzzle has to its predetermined final design. Only the addition of the missing fragments of the puzzle would reveal if the picture was as he guessed it would be.”
—Stanley Kubrick (b. 1928)
“Your notions of friendship are new to me; I believe every man is born with his quantum, and he cannot give to one without robbing another. I very well know to whom I would give the first place in my friendship, but they are not in the way, I am condemned to another scene, and therefore I distribute it in pennyworths to those about me, and who displease me least, and should do the same to my fellow prisoners if I were condemned to a jail.”
—Jonathan Swift (16671745)
“My consolation is to think of the women I have known, now that there is no longer such thing as elegance. But how can people who contemplate these horrible creatures under their hats covered in pigeon-houses or gardens, how can they understand the charm of seeing Madame Swann wearing a simple mauve cap or a small hat surmounted by a straight iris?”
—Marcel Proust (18711922)