Maze Theory


Since I was a child I have been intrigued by a single line spoken by the villian du jour on an old rerun of the Adam West Batman TV Series. You see, the villian (I don't now recall which one) had kidnapped Robin and told Batman that Robin was tied up in the center of a maze. The Caped Crusader had a choice of either finding Robin or pursuing the villian before the next crime is committed.

Naturally Batman chooses to save Robin. He navigates the maze easily in the span of a commercial break, and unties the Boy Wonder. Just then, the arch-villian and a few henchmen (does every villian get their henchmen from the same temp agency?) appear in a hole in the ceiling far above the Dynamic Duo. The villian congratulates Batman on locating Robin, but adds "Now that you've found your way to the center of the maze, Batman, you'll NEVER find your way out!" (or words to that effect.) After some gratuitous maniacal laughter, the villian and henchmen leave to go commit that crime that was alluded to earlier, without a care in the world, secure in the knowledge that Batman and Robin are trapped in the maze forever. (Yeah, right!)

Of course Batman shows up in time to foil the crime - much to the astonishment of the villian du jour (Why are they always so surprised to see Batman survive?) - but the damage was done. I had already heard the phrase "Once you reach the center of the maze, you will NEVER find your way out." Is such a maze possible? I put the question on hold for a decade or two while I went about the business of growing up and having a life.

So here I am, in my early 30s, and suddenly interested in mazes again. That line from an old TV show came back to me. What is the "center" of a maze, and is an unsolvable maze even possible? In my research, I have determined that the only way to make a maze unsolvable is to alter the layout of the maze after Batman enters it. The villian may have had this done, but I don't remember for sure. Even so, could I design a maze that truly fits this description passively, without actively playing tricks on whomever goes inside it? Let's examine that question.

Impossible to Solve?

Every maze has a goal. Sometimes the goal is to enter through one doorway and exit through a separate doorway. This is usually found in puzzle books. Sometimes the goal is to reach some point inside the maze and return safely through the same doorway that you entered. This seems to be the construction of most mazes built large enough for a person to walk through.

What makes a maze difficult to solve? If there is but a single path to follow with no intersections, no decisions to make, then the maze may be time-consuming, but not difficult. It's really a no-brainer. Such "unicursal labrynths" have been cut into the turf in Great Brittan for centuries. While this will provide a nice quiet stroll in a minimal amount of space, it is not what we are looking for.

What we want here is the opposite end of the spectrum - the greatest number of intersections and decisions possible. More intersections means more decisions for the maze walker to make. The more decisions to make, the greater the likelyhood for mistakes and getting "lost". (The maze cannot be made impossible to solve, but we can make it a more difficult challenge.) To improve the number of intersections, either the amount of real estate the maze is built upon needs to be as large as possible, or the space must be utilized as efficiently as possible by making the walls thin and the corridors narrow.

We can also increase the number of choices to make at some intersections. This would add to the confusion by turning a "left or right" decision into a "left, right or straight ahead" decision. We cannot make all of the decisions that diffucult, or else we will end up with a field of pillars. Remember that many decisions will have to carry the solver far away from the decision just made before another decision needs to be made. The time lag here will help to cloud the short-term memory, and make remembering where you are and how you got there more of a mystery.

A more advanced trick is to place the same pattern of intersections at several locations throughout the maze. This will help lead the would-be solver to think that they have been this way before and lead to total disorientation when they run into a dead end. The effect can be enhanced with the clever placement of embellishments such as benches, statues and fountains. (Let's see...I took a right at the statue of Aphorditie, and a left at the fountain...Didn't there used to be a corridor here?...What the-?)

The Center of the Maze

Now let's address the other part to the favorite phrase - What is the center of the maze? Is it the geographic midpoint of the real estate the maze is built on? Probably not, as that point may turn out to be some non-descript piece of corridor. Any part of a maze that deserves it's own title should be a prominent figure, easily recognizable as such both from inside the maze and by looking at a plan view. The "center" may, in fact be located in the middle of the real estate, but there is no reason that it must.

It seems to me that the "center" would probably be some type of chamber or room located at the deepest heart of the puzzle, with the greatest number of intersections between there and the exit. (If Batman found the center so rapidly, then what makes the villian think that backtracking would be such a challenge for him? Nevermind. It doesn't matter. Where were we?) If the "center" has but a single path leading into it, then finding your way out of a room with only a single exit is no challenge. To give it some bite, the "center" ought to have more than one way out.

Where would the other doors go to? Some might lead back into the maze that you just came out of. Some might lead to dead ends, forcing the solver to return to the center. Some might lead back into the center through a different doorway than the one the solver just used to exit the center a few minutes before. The most challenging maze will have some combination.

If you wander into a room that you recognize as the "goal" of the maze, then deciding that you should turn around and go back home is simple to do by leaving through the door that you came in, no matter how many doors the room has. As a maze feature, the "center" - more correctly called a "hub" if there are multiple ways out - will not reach it's full glory as an obstacle to the solution unless the solver is forced to pass through the hub en route to some place else. This means a double threat for the solver - once on the way in, and again on the way out.

This forces the puzzlemaker to put at least one goal into the maze at a point beyond the hub. The goal is probably also a room of proportions similar to those of the hub, but this restriction is not mandatory. The goal (or new "center"?) may be empty, or may contain a statue, fountain, benches, vending machine (A what?!?) or whatever strikes the designer's fancy.

Finished Design Proposal

Of course, the puzzle can be compounded further by increasing the number of hubs and/or goals. When a person enters a hub, they will always ask themselves if this is the hub they just left, or the other one. (Insert gratuitous maniacal laughter here.) With that in mind, here is my proposal for a devious little maze:

  • Rectangular, covering an entire acre
  • Walls are formed of tall shrubbery with a chain-link fence inside to prevent "shortcuts"
  • Brick-paved walkways wide enough for two wheelchairs to pass in opposite directions
  • One entrance (with a one-way turnstyle)
  • A separate exit (also with a one-way turnstyle)
  • Two hubs (Identical, eight sides, eight dorways, 20 ft between opposite walls)
  • One goal (same dimensions as the hubs, but only one doorway)
  • Plenty of benches, statues and water fountains throughout for that special tranquil ambiance (and to help confuse)
In addition, I propose that a second maze be built inside of the primary maze. The second maze would be simpler, with very few decisions to make, all dead ends would become obvious as soon as someone gets to the intersection, and a brain-dead chimp with a wooden leg should be able to complete it in under 5 minutes. The purpose of the simpler maze is to allow people who do not have the patience, sense of direction, or physical stamina to complete the large maze an opportunity to experience the maze, without having to enter the "real" maze. The more difficult maze could easily be built around the smaller maze, or bumped up next to it.

As a finishing touch, there could also be lights embedded in the edges of the walkways. These glowing accent lights could give the maze an underlit glow when they are shining steady. If the lights were wired to permit it, they could "chase" in a pattern that would lead people out of the maze from wherever they are. (Like runway lights.) Perhaps they could also chase in reverse, leading into the goal.

And now for something completely different...

In 3D!

Even though the maze description laid out so far is for the enjoyment of walking through, and not merely for tracing with pencil on a piece of paper, the layout is still essentially two-dimensional. Oh, sure, some advanced maze designers have added walkways to their designs that allow the solver to cross over other paths without creating an intersection. They refer to this innovation as three dimensional maze-building. That's a wonderful improvement, but the majority of the maze still exists on a 2D plane. I say why not take this concept farther, constructing the maze entirely out of overhead platforms, catwalks, ladders, stairways and elevators?

Each platform could be at a slightly different elevation, and the walkways could slope up or down slightly to compensate for the change in elevation. The same slope found on handicapped access ramps should be sufficient. With elevators providing an altitude assist, the majority of the solution (if indeed not the entire solution) could be entirely downhill. This would allow wheelchair-bound puzzle enthusiasts to participate without wearing out either their arms or batteries. The proper solution would involve several rides up in multiple elevators. This overhead maze could be built to resemble platforms suspended in Giant Redwood trees with elevators hidden in the trunks. Suspension cables can be disguised to resemble vines. Of course, underneath it all would be solid steel and concrete construction. (Have I gone too far yet? Let's try.)

To add to the illusion of climbing around in the branches of a forest, the forest floor could be covered with a hedge maze. Below that, there could be a cave that leads down to tunnels in the basement of the whole complex (built of reinforced concrete tubes) that become an underground labrynth lit with faux torches and resembling underground caverns. The entire three-maze complex could be populated with animitronic faries in the treetops, talking flora and fauna on the ground, and trolls and hobgoblins under the surface, thus giving the entire attraction a Fairy Tale atmosphere.

While we're at it, there could even be some sort of story that unfolds as the puzzles are solved. Perhaps a story about the kidnap of the Fairy Queen by the trolls, and her subsequent rescue by the mazegoer. (Didn't Walt Disney start out this way?) Look, if you're gonna dream, why not dream big? Dreaming has no construction budget. No, I don't expect anyone will ever build it, but that's not the point. In my mind, there are adults and kids of all ages enjoying the mazes that I have outlined here. It looks nice from my viewpoint.

Perhaps one day I will create illustrations to go with this narrative. These fictional environments could be rendered on a home computer for no cost and little effort, but will probably not be accomplished soon.

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