Abstract

Smullyan poses a problem in the familiar genre of knights (who always tell the truth) and knaves (who never tell the truth). Although a solution of sorts is presented, evading the difficulty without confronting it, the central difficulty is by no means resolved. In this paper, I will analyze the problem and present two solutions, one of which I prove to be the most efficient algorithm to solve Smullyan's problem. Though it will later be necessary to alter the problem, for the moment let me present it exactly as Smullyan originally gave it with the following excerpt from Satan, Cantor and Infinity, in which the character Alexander meets with King Zorn after deducing the location of his kidnapped love, the princess Annabelle.

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