Truth-Teller–Liar Puzzles with Self-Reference

Laith Alzboon and Benedek Nagy
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Laith Alzboon: Department of Mathematics, Eastern Mediterranean University, Famagusta, North Cyprus, via Mersin 10, Gazimağusa 99450, Turkey
Benedek Nagy: Department of Mathematics, Eastern Mediterranean University, Famagusta, North Cyprus, via Mersin 10, Gazimağusa 99450, Turkey

Mathematics, 2020, vol. 8, issue 2, 1-12

Abstract: In this paper, we use commonsense reasoning and graph representation to study logical puzzles with three types of people. Strong Truth-Tellers say only true atomic statements, Strong Liars say only false atomic statements, and Strong Crazy people say only self-contradicting statements. Self-contradicting statements are connected to the Liar paradox, i.e., no Truth-Teller or a Liar could say “I am a Liar”. A puzzle is clear if it only contains its given statements to solve it, and a puzzle is good if it has exactly one solution. It is known that there is no clear and good Strong Truth-Teller–Strong Liar (also called SS) puzzle. However, as we prove here, there are good and clear Strong Truth-Teller, Strong Liar and Strong Crazy puzzles (SSS-puzzles). The newly investigated type ‘Crazy’ drastically changes the scenario. Some properties of the new types of puzzles are analyzed, and some statistics are also given.

Keywords: SS-puzzles; SSS-puzzles; Crazy people; self-contradictory statements; puzzle-graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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