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Stuck In A Maze?

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The stunningly simple rule that will always get you out of a maze

You thought the maze looked fun, but now you can’t find your way out. Luckily, mathematics is here to help you escape, says Katie Steckles

GETTING lost in a maze is no fun, and on that rare occasion when you find yourself stuck in one without a map or a bird’s-eye view, it can be difficult to choose which way to go. Mathematics gives us a few tools we can use – in particular, topology, which concerns shapes and how they connect.

The most devious mazes are designed to be as confusing as possible, with dead ends and identical-looking junctions. But there is a stunningly simple rule that will always get you out of a maze, no matter how complicated: always turn right.

Any standard maze …

can be solved with this method (or its equivalent, the “always-turn-left” method). To do it, place one hand on the wall of the maze as you go in, and keep it there. Each time you come to a junction, keep following the wall – if there is an opening on the side you are touching, take it; otherwise, go straight. If you hit a dead end, turn around and carry on.

The reason this works is because the walls of any solvable maze will always have at least two distinct connected pieces: one to the left of the optimal solution path (shown in red), and one to the right. The section of wall next to the entrance is part of the same connected chunk of maze as the wall by the exit, and if you keep your hand on it, you will eventually walk along the whole length of the edge of this object – no matter how many twists and turns this involves – and reach the part at the exit.

While it is guaranteed to work, this certainly won’t be the most efficient path – you might find you traverse as much as half of the maze in the process, or even more depending on the layout. But at least it is easy to remember the rule.

Some mazes have more than two pieces. In these, disconnected sections of wall (shown in yellow) inside the maze create loops. In this case, if you start following the wall somewhere in the middle of the maze, there is a chance it could be part of an isolated section, which would leave you walking around a loop forever. But if you start from a wall that is definitely connected to the outside, wall-following will still get you out.

It is reassuring to know that even if you are lost in a maze, you can always get out by following some variation on this rule: if you notice you have reached part of the maze you have been to before, you can detect loops, and switch to the opposite wall.

This is especially useful for mazes where the goal is to get to the centre: if the centre isn’t connected to the outside, wall-following won’t work, and you will need to switch walls to get onto the centre component. But as long as there are a finite number of pieces to the maze, and you keep trying different ones, you will eventually find a piece that is connected to your goal. You might, however, miss the bus home.

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4 COMMENTS

  1. Maori invented this method 1250AD… Thats how they remained marooned here.

    If you turn right as soon as you enter that maze youre on one hell of a journey until you finally get back to the start.

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  2. In 2019 a group of us went on a M/C trip to the south Island and ended up at the puzzle world on the outskirts of Wanaka, a half dozen of us went through the maze at that place, between the 10 year old daughter of a mate and myself we breezed through it in no time and were standing on an observatory looking down at the action at the end of the maze when my mates daughter started taunting her dad big time ,now this is the cookie bear slapper I’m talking about so I said to the her “don’t do that to much” but she just kept on at it ,everytime he came to a dead end she’d be yelling shit at him until finally he spat the dummy and started yelling back at her with Fs and little bitches and the occasional C.
    It was that embarrassing that I pissed off down to the carpark that runs down the side of the building , a couple of minutes later his daughter came out still in hysterics, about 10 minutes later he emerged red faced but not saying a word about the episode at all and being a good mate I to have never mentioned it again except for everytime we have a beer together, LOL.

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  3. The key to not being caught in a societal or political maze, is to never enter it in the first place. In these mazes the walls keep changing. You are no more than a Lab rat being driven to exhaustion in some sick game.

    Avoiding the maze in the first place is the hardest part:

    “Squeak, squeak. Oh look there’s a piece of cheese / lock down payments / $ for research / $ for Maori hakas / $ for woke poetry / $ for children’s bodily mutilation / $ for unused cycle lanes / $ for studying the climate in the Truman Show / KFC / UBI.

    It’s just inside that doorway and off to the left. Let’s follow the trail of free breadcrumbs.”

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  4. The matrix, to make the choice about real, “truth” world or the “artificial” paradisiacal world.

    To get out of that maze, will you take the 💊 & harden up,
    Or the blue pill 🦠 (turns green on publishing) like taking the 💉 to weaken & sicken all those about you, 🤢 🤮

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