The Complexity and Difficulty of a Maze

Michael Scott McClendon
Bridges: Mathematical Connections in Art, Music, and Science (2001)
Pages 213–222


Some mazes are more difficult to solve than other mazes. For this reason. we develop a method by which the difficulty of a maze can be quantified, In the process we determine a way in which the complexity of the hallways in a maze, which is the degree to which a maze has short and quick twists and turns, can also be measured. We use the various complexity measures of the hallways in a maze in order to calculate the overall complexity and difficulty of the maze. We provide several examples in order to help establish some validity of the formulas developed in this paper. As the main tool used in developing our methods is continuum theory, we will use appropriate definitions throughout this paper.