A circular maze

Image by PublicDomainPictures from Pixabay 

What makes something a maze?

Google Dictionary says that a maze is “a network of paths and hedges designed as a puzzle through which one has to find a way.” Similarly, a labyrinth is “a complicated irregular network of passages or paths in which it is difficult to find one’s way; a maze.” It’s a place meant to confuse you, a place where you’re meant to get lost. And the odd thing about it is, it’s fun. Have you ever been in a corn maze? How long did it take you to find your way out?

Mazes show up in mythology and folklore a lot. The most famous one is the labyrinth created by Daedalus for the Minotaur on the Greek island of Crete. Mazes also show up throughout the world, including Scandinavia.

They’re made of stone or hedges or just mounds of earth. They’re cut into crops or turf. They’re carved on stone, painted on walls, inlaid in floor mosaics, minted on coins, woven into cloth. Why are we so fascinated by mazes?

Well, if you’ve ever gotten lost in a store, or been frustrated driving through a city with lots of one-way streets, or lost your bearings while hiking in the woods, I’m sure you found yourself wishing there was an easy way to find your way out, short of scattering breadcrumbs like Hansel and Gretel.

The nice thing about mazes is that they follow rules, and if you know the rules, you can use them to get out. All of the mazes shown above can be solved using the right-hand rule (which is also a rule that you use in physics in a very different context). As you enter the maze, put your right hand on the wall. Keep following the wall. Since those mazes are one continuous line, you will eventually end up back at the entrance. This works with just about any maze that has an outer boundary, including corn mazes. It’s the long way around, certainly, since you’ll end up walking every single pathway in the maze, but it’ll get you there.

But what if the rules are a little different? In An Elf’s Equations, I have three mazes. The first, in the Sylvan Vale, is a maze that you can’t solve without knowing the Fibonacci sequence (or someone tells you the sequence of steps to take). The second maze, around the World Tree in Vanaheim, is a very logical, squared-off maze full of right angles and dead ends. The right-hand rule would work just fine in there, but it’s straightforward enough that you’d likely be able to walk through it easily.

And then there’s the maze of Pthagor, the math dragon. It looks so simple at first.

A deceptively easy maze

You could just walk right through this, right? Ah, but there’s a catch, as Sagara and her friends discover:

At the mouth of the cavern, they found a sign printed in several different languages, including Vanir runes, Dragon script, Canto, English, and several more they did not recognize. It read:

          To go forward, turn only to the right.

“What does that mean?” Petunia asked. “If it’s a riddle, I don’t get it.”

“I think it’s instructions,” Max replied.

Cretacia snorted. “And what if we don’t go right?”

“One way to find out,” Sagara said, and she strode into the cavern.

Before her, laid out on the smooth floor, a maze had been marked out in faintly glowing paint. At first, she thought it was a simple square maze, like the one in the Vanir garden of the World Tree, but then she looked again. From the entrance, paths went left, straight and right. They branched and turned. About fifty feet away, Sagara could see the exit, leading deeper into the cavern.

“Ha!” Cretacia yelled. “Easy!” She ran straight into the maze, heading for the exit, but when she crossed one of the painted lines, she disappeared.

“Cretacia!” Millie squealed.

“Great horny toad warts!” Cretacia said behind her. “That was really weird. One second, I was in there, and the next second, I was back out here. I wonder what happens if I turn left?”

“No, wait,” Sagara said, but Cretacia had already run into the maze and took the first left turn. Again, she disappeared.

“Hey!” came her voice from above. “How do I get down from here?”

Sagara stepped back from the cavern mouth and found Cretacia sitting on the bulbous tip of the troll’s nose.

— pp. 233-4

A map of a logic maze outside the Tekniska Museet in Stockholm.I based this maze on one I encountered outside the Tekniska Museet in Stockholm. It’s a tricky maze because it has different rules. Can you find your way through it? The solution to Pthagor’s maze is in An Elf’s Equations.

Now here’s the activity: what other rules can you change to make a maze more tricky? Maybe you can only turn if you can’t go straight any more, or you have to turn if you can, or you have to jump over things. Try making a maze of your own with different rules! Can you make something that looks simple but is actually hard to get through? If you do, take a picture and share it with me either here or on my Facebook page. I’d love to see your creations!

And if you’re wondering what that troll’s nose looked like, here’s a troll I found under a bridge in Seattle (well after I’d written this scene!) who was friendly and obliged me when I asked for a selfie with him.

Troll sculpture under a bridge in Seattle