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Crazy Truth-Teller–Liar Puzzles

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Abstract

In this manuscript, we define and discuss a new type of logical puzzles. These puzzles are based on the simplest truth-teller and liar puzzles. Graphs are used to represent graphically the puzzles. (The solution of) these logical puzzles contain three types of people. Strong Truth-tellers who can say only true statements, Strong Liars who can make only false statements and Weak Crazy people who must make at least one self-contradicting statement if he/she says anything. Self-contradicting statements are related to the Liar paradox, such that, there is no Truth-teller or a Liar could say “I am a Liar”. In any good puzzle there is a unique solution, while the puzzle is clear if only the people of the puzzle and their statements are given to solve the puzzle. It is well-known that there is no good and clear SS-puzzle (Strong Truth-teller-Strong Liar puzzle). However, in this paper, we show that there are clear and good SSW-puzzles. Characteristics of the newly investigated type of people, the ‘Weak Crazy’ people, has also been studied. Some statistical results about the new type of puzzles and a comparison with other types of puzzles are also shown: the number of solvable and also the number of good puzzles is much larger than in the previously known SS-puzzles.

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Acknowledgements

Comments of the anonymous reviewer are gratefully acknowledged.

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This research received no external funding.

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  1. Department of Mathematics, Eastern Mediterranean University, via Mersin 10, Famagusta, North Cyprus, Turkey

    Laith Alzboon & Benedek Nagy

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  1. Laith Alzboon
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  2. Benedek Nagy
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Correspondence to Benedek Nagy.

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Alzboon, L., Nagy, B. Crazy Truth-Teller–Liar Puzzles. Axiomathes 32, 639–657 (2022). https://doi.org/10.1007/s10516-021-09546-7

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  • DOI: https://doi.org/10.1007/s10516-021-09546-7

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