Logical Puzzles

In this thesis, we use commonsense reasoning and graph representation to study two different new types of logical puzzles with three types of people. In the first type of puzzles, any person in the puzzle can be either Strong Truth-teller, Strong Liar or Strong Crazy. While in the second type, any person in the puzzle can be either Strong Truth-teller, Strong Liar or Weak Crazy. Strong Truth-tellers say only true atomic statements, Strong Liars say only false atomic statement and Strong Crazy people say only self-contradicting statements, while Weak Crazy person must say at least one self contradictory statement if he/she say anything. 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 only the statements of its people are given 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, in this thesis, we show that there are good and clear Strong Truth-teller, Strong Liar and Strong Crazy puzzles (SSS-puzzles) and Strong Truth-teller, Strong Liar and Weak Crazy puzzles (SSW puzzles). The newly investigated types Weak and Strong ‘Crazy’ changes drastically the scenario of SS-puzzles. Some properties of the new types of puzzles are analyzed and some statistics are also given. Also we provide a comparison between the three different types of puzzles along with characterization of graph representation of good puzzles of the new types of puzzles. Keywords: SS-puzzles; SSS-puzzles; SSW-puzzles; Strong Crazy persons; Weak Crazy persons; Self-contradictory statements; Graph representation of the puzzles.