Mazes

A maze is a complex tour puzzle in the form of a complex branching passage through which the solver must find a route. In everyday speech, both maze and labyrinth denote a complex and confusing series of pathways, but technically the maze is distinguished from the labyrinth. The labyrinth has a single through-route with twists and turns but without branches; it is not designed to be as difficult to navigate as a maze is. The pathways and walls in a maze or labyrinth are fixed (pre-determined). Maze-type puzzles where the given walls and paths may change during the game are covered under the main puzzle category of tour puzzles. The Cretan maze is the oldest known.

Maze solving is the act of finding a route through the maze from the start to finish. Some maze solving methods are designed to be used inside the maze by a traveler with no prior knowledge of the maze, whereas others are designed to be used by a person or computer program that can see the whole maze at once.

The mathematician Leonhard Euler was one of the first to analyze plane mazes mathematically, and in doing so made the first significant contributions to the branch of mathematics known as topology.

Mazes containing no loops are known as "standard", or "perfect" mazes, and are equivalent to a tree in graph theory. Thus many maze solving algorithms are closely related to graph theory. Intuitively, if one pulled and stretched out the paths in the maze in the proper way, the result could be made to resemble a tree.

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