Counting Variations of Knights and Knaves Puzzles

Presenter(s)

Taisha Charles

Abstract or Description

This project focuses on the enumeration of Knights and Knaves Puzzles, which are logic-based puzzles where n-trolls make a statement on the number of Knights and Knaves in the puzzle. Knights are trolls who only tell the truth and Knaves are trolls who only lie. This research was inspired by Levin and Roberts’ previous research on the classic variation of the puzzle. We determined how many classic puzzles have no solution and how many have a unique solution when the number of trolls is less than seven. We also considered two variations on the classic version of the puzzle; a disjunction variation in which trolls can make “or” statements and a Neutral variation in which a troll is either a Knight, Knave, or Neutral, a troll who makes sometimes true, sometimes false statements. We determined the number of puzzles, the number of solutions, and the number of max solutions for each variation, as well as other such questions that Levins and Roberts brought up in their paper. We created expressions quantifying these answers by listing puzzles and their solutions and then following along for trends in the data. This research was sponsored by the ACRE, Albright Creative Research Experience, program.