The Hardest Logic Puzzle Ever

The Hardest Logic Puzzle Ever is a logic puzzle invented by American philosopher and logician George Boolos and published in The Harvard Review of Philosophy in 1996. A translation in Italian was published earlier in the newspaper La Repubblica, under the title L'indovinello piĆ¹ difficile del mondo. The puzzle is inspired by Raymond Smullyan.

It is stated as follows:

Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.

Boolos provides the following clarifications:

  • It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
  • What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
  • Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.

Read more about The Hardest Logic Puzzle Ever:  History, The Solution, Unanswerable Questions and Exploding God-heads, See Also

Famous quotes containing the words puzzle, hardest and/or logic:

    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 (1874–1963)

    By the time we hit fifty, we have learned our hardest lessons. We have found out that only a few things are really important. We have learned to take life seriously, but never ourselves.
    Marie Dressler (1873–1934)

    “... We need the interruption of the night
    To ease attention off when overtight,
    To break our logic in too long a flight,
    And ask us if our premises are right.”
    Robert Frost (1874–1963)