A general form on the logic puzzles of Boolos (Logic, Algebraic system, Language and Related Areas in Computer Science)

Abstract

Boolos (1996) posed the puzzle "The hardest logic puzzle ever" which had been devised by Raymond Smullyan, and gave a solution in the style of biconditional questions. We introduce a simple formalization of the puzzle consisting of questions, answerers, and answers in terms of propositional logic, and show its adequacy by the truth values (0, 1) semantics. Then it turns out that the hardest logic puzzle can be considered as a natural extension of the puzzles of knights and knaves, i.e., lying and truth-telling by Smullyan. Here, we pose a general form of the puzzle, and provide partial solutions to some of the instances.