Arts & Culture

How to Solve Mazes: Part One

Thomas Edison once said, “I have not failed.  I’ve just found ten thousand ways that won’t work.”  This neatly expresses the first and most important tip for solving mazes:  no matter what, perseverance will always solve a maze.  The time spent running into dead ends is still time spent working toward the goal –– and not many mazes have ten thousand dead ends.  Solving a maze is not like inventing a perpetual motion machine –– a solution is guaranteed.  This is helpful to remember especially when attempting particularly long mazes, or mazes with unusual elements.  It can encourage the most frustrated efforts to discover well-hidden pathways.

Second, no one should worry about starting at the point marked Start.  Some people consider this a cheap trick, but in reality, there is no way to regulate against backwards solving.  I discovered this the hard way when I was about nine, and I created a maze that looked something like this:  My older and wiser cousin quickly figured it out by solving from the bottom up, a tactic I had never considered.  Try it and see if you can find what made this maze so much easier to solve backwards.  

Because so many people use this tactic, smart maze crafters know to make their mazes just as difficult to solve starting from the end as the beginning (occasionally starting from the end is actually harder).  So why start from the end, if that idea is already anticipated?  First of all, it is often easier.  But more likely, the experienced solver might start two separate lines, one from Finish, the other going from Start.  This approach can make the task easier by strategically avoiding large branches of paths.

This sequence shows the process of solving a maze with this tactic:

The first picture shows the solver’s first line attempt.  Beginning at Start, he finds the correct path fairly easily for a while, but the line stalls at a rather overwhelming junction of six pathways.  Rather than take the time to scope out each of these paths separately, the solver decides to begin another line from the finish (picture 2), which is likewise straightforward until running into a baffling fork in the road.  Looking back at the line from Start, he realizes that, since the two lines need to connect somehow, the three downward pathways at that junction (marked here with red X‘s) must not be correct.  He points the line toward one of the two remaining path choices, and one of those, as seen in the last picture, winds around the top of the maze and solves it.  Starting from both the beginning and the end can help, indeed.

A third tip for solving mazes assists primarily with mazes made by people, which in general far outrank computer-generated mazes in the qualities of difficulty and entertainment.  If a human being has made the maze you try to solve, intending to challenge and entertain you, think like that human being.  A good maze crafter anticipates the solver’s thoughts at different parts of the maze and draws it accordingly.  Take advantage of this –– be leery of those enticing paths and seek out disguised ones.  Also, find out about the maze-maker’s habits.  My cousin used this against me when solving the earlier maze example.  In case you didn’t notice, I had consistently arranged passages like this:

I always forked into two paths at a time, and at any given fork, the path to start pointed upwards, making the path choices obvious.  My cousin knew my tendencies and used that knowledge to her advantage.  Computer-generated mazes, on the other hand, have no such predictability, excepting only their inherent randomness, but this very randomness gives them fatal defects –– simplicity of pathways, and consequently, minor enjoyability.  Although not always helpful, this technique is quite useful when the solver either knows the maze crafter well, or knows his mazes well, after solving many of them.  Every maze crafter has habits.  

Remember these three tips as conveniences for quickly solving mazes –– think like whoever made the maze, start from the finish, and most importantly, persevere.

This month, I have provided a bumper crop of two mazes, in keeping with the Thanksgiving festivities:

This maze is old but can still be reasonably difficult:

 

And a bonus maze:  I got carried away when doing one of the examples for this article and made it too long, so here it is!

 

Works Cited

“Thomas A. Edison Quotes.” Goodreads, Goodreads, https://www.goodreads.com/author/quotes/3091287.Thomas_A_Edison?page=1. 

 

Image Credit:  Rees Pingel

Note:  the quote at the beginning of the article is the most common paraphrase of one of Edison’s statements, and is not exact.

 

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