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Truth-Teller–Liar Puzzles with Self-Reference

Author

Listed:
  • 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)

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.

Suggested Citation

  • Laith Alzboon & Benedek Nagy, 2020. "Truth-Teller–Liar Puzzles with Self-Reference," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:190-:d:316436
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