The Hardest Logic Puzzle Ever is a logic puzzle so called by American philosopher and logician George Boolos and published in The Harvard Review of Philosophy in 1996.[1][2] Boolos' article includes multiple ways of solving the problem. A translation in Italian was published earlier in the newspaper La Repubblica, under the title L'indovinello più difficile del mondo.
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,[3] in some order. You do not know which word means which.
Boolos provides the following clarifications:[1] a single god may be asked more than one question, questions are permitted to depend on the answers to earlier questions, and the nature of Random's response should be thought of as depending on the flip of a fair coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.[4]
^ abBoolos, George (1996). "The hardest logic puzzle ever" (PDF). The Harvard Review of Philosophy. 6: 62–65. doi:10.5840/harvardreview1996615. Archived from the original (PDF) on 30 January 2023.
^Kazmi, Kumail (April 14, 2021). "The Hardest Logic Puzzle Ever? (with Answer)". Puzzleness - Encyclopedia of Puzzles. Puzzleness. Retrieved April 14, 2021.
^Da means yes in Russian, ja means yes in German.
^Note that the Random god in Boolos' puzzle is a god who acts randomly as either a truth-teller or a liar. This is different from a god who answers 'yes' or 'no' randomly. One usual trick in solving many logic puzzles is to design a (perhaps composite) question that forces both a truth-teller and a liar to answer 'yes'. For such a question, a person who randomly chooses to be a truth-teller or a liar is still forced to answer 'yes', but a person who answers randomly may answer 'yes' or 'no'.
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