The simplest technique for solving many labyrinths involves keeping one hand on a wall and following it until you find the exit.
This "wall follower" method works remarkably well for many types of mazes. Here's a breakdown:
The Wall Follower Method
The core principle is straightforward:
- Choose a Wall: Pick either the right or left wall and stick with it throughout the entire maze.
- Keep Your Hand on the Wall: As you navigate, maintain physical contact with the chosen wall.
- Follow the Wall: Whenever you encounter a choice, continue following the wall in the same direction (right or left, depending on your initial choice).
- Eventually, You Should Escape: With this consistent approach, you should eventually reach either the end or the beginning.
Why It Works (and When It Doesn't)
The wall follower method is guaranteed to work if the entrance and exit are on the outer walls, and the maze is simply connected (meaning there aren't disconnected walls within the maze). In essence, the maze must not have any paths which loop back and create an isolated "island" in the middle.
However, the wall follower method fails in mazes with:
- Disconnected Walls (Islands): If the maze has sections that are entirely separate from the outer walls, the wall follower may simply circle endlessly within that disconnected section without reaching the exit.
- Entrance and Exit Not on Outer Walls: If the start and end point are in the middle of the maze.
Alternative Strategies
When the wall follower method fails, you might need other strategies:
- Trial and Error: Randomly selecting paths and backtracking when you reach dead ends.
- Pencil and Paper: Mapping out your progress to avoid repeating mistakes.
- Algorithm-Based Approaches: More complex strategies include the Pledge Algorithm and Trémaux's Algorithm, which are suitable for computer programs or very complex mazes.
Example
Imagine a simple maze with a clear path from entrance to exit along the outer wall. Using the "right-hand rule," you'd place your right hand on the wall at the entrance and simply follow that wall until you find your way out.
In conclusion, while the "wall follower" method is a great starting point for solving many labyrinths, its effectiveness is limited by the maze's design. Understanding these limitations and exploring alternative strategies is crucial for tackling more complex mazes.
