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% probability ... 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:
“Scholars and artists thrown together are often annoyed at the puzzle of where they differ. Both work from knowledge; but I suspect they differ most importantly in the way their knowledge is come by. Scholars get theirs with conscientious thoroughness along projected lines of logic; poets theirs cavalierly and as it happens in and out of books. They stick to nothing deliberately, but let what will stick to them like burrs where they walk in the fields.”
—Robert Frost (18741963)
“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)
“There is the rich quarter, with its houses of pink and white, and
its crumbling, leafy terraces.
There is the poorer quarter, its homes a deep blue.
There is the market, where men are selling hats and swatting flies”
—John Ashbery (b. 1927)