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Find a way through the puzzle
A maze is a tour puzzle in the form of a complex branching passage through which the solver must find a route. This is different from a labyrinth, which (strictly speaking) has an unambiguous through-route and is not designed to be difficult to navigate (despite the common uses of the word to indicate various complex, confusing structures).
The pathways and walls in a maze or labyrinth are fixed. 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 mathematician Leonhard Euler was one of the first to analyse plane mazes mathematically, and in doing so founded the science of topology.
The following algorithms are designed to be used inside the maze by a traveler with no prior knowledge of the maze's layout. There are other algorithms that can be used for solving paper mazes, where the solver has an overview of the maze.
The wall follower, the best-known rule for traversing mazes, is also known as either the left-hand rule or the right-hand rule. If the maze is simply connected, that is, all its walls are connected together or to the maze's outer boundary, by keeping one hand in contact with one wall of the maze you are guaranteed not to get lost and will reach a different exit if there is one; otherwise, you will return to your entrance. If the maze is not simply connected, this method will not help you to find the disjoint parts of the maze.
Wall following can be done in 3D or higher dimensional mazes if you project its higher dimensional passages onto the 2D plane in a deterministic manner. For example, in a 3D maze pretend up passages actually lead northwest, and down passages actually lead southeast, and then apply the standard wall following rules.
Flags: Very Short (0-60 mins), Solo, Children, Teens, Adults, Seniors, Indoors, Outdoors, At Home, Morning, Day, Night, Sunny, Snowy, Rainy