Mazes seem to hold a bizarre fascination for human beings; how else to you explain their inclusion in Greek myth, which usually has space for little that is more mundane than a god who transforms himself into an animal in order to seduce women or possibly a big war? What possible reason do hundreds of people have for flocking to places like Hampton Court to wander among near-identical hedgerows in desperate search of a bench, rather than attempting a similar feat in the air-conditioned surrounds of IKEA? Well, this article isn't going to answer that, but instead it will answer the equally important question of what to do if you need to negotiate a maze.

The methods described in this entry are guaranteed to work only in a maze that is free from such obstacles as force fields, water hazards, one-way systems and bull-headed creatures with chips on their shoulders. They may, however, contain bridges, tunnels and loops where it is possible to go round in a circle. No secret passages, though.

The Left-hand Method

If you place your left hand on the left-hand wall upon entering a maze, and follow that wall all the way around, never removing your hand, you will, after a tour of numerous culs-de-sac, arrive at an exit. This very famous method is somewhat over-rated, as there is no certainty that the exit will actually be the goal - rather you are quite likely to find yourself right back where you started. Of course, if your goal is merely to not get lost in the maze this is a perfectly decent tactic, although an even better one is not to enter the maze in the first place.

There is one notable circumstance under which this method is guaranteed to work, that is if the maze is all on one level and both the exit and entrance are located in the outer wall.¹ In this case you will simply follow the outer wall, going round any walls that stick out from it, until you reach your goal. More generally, if there are several gaps in the outer wall then you will find yourself one gap clockwise from the one at which you entered. All this advice does assume the maze is possible to complete, but if it isn't then you haven't really got a maze, more two mazes with an outer wall in common. That and a maze-designer with a poor sense of humour.

Note: It also works if you put your right hand on the right-hand wall and follow that around instead. Or you could follow a wall without touching it with any part of your body; just make sure you don't skip over any gaps.

The Marking Method

A useful thing to do when exploring a maze is to mark off any bits that you have already visited and found to be nothing but dead-ends. By gradually cutting off more and more of the maze with your lines of chalk (or whatever) you must eventually find yourself at the exit. Or possibly the entrance, as this method will work from a point somewhere in the middle. Should this happen, you can pretend the entrance isn't there and keep going until you do reach the exit. Here is one suggested algorithm of how to mark the maze:

One: When you come to a new junction, mark the path you entered by with an arrow pointing back the way you came. Now set off down any unmarked path.

You do this because you don't want to go back until all the other branches have been explored.

Two: If you come to a dead end, backtrack. If you come to a junction you have already visited, draw a line across your path and backtrack.

Don't keep exploring when you've gone round in a circle - you need to go back and eliminate any side passages first.

Three: When you backtrack to a junction, draw a line across the path you just came down and choose another unmarked path to explore (and go back to instruction one). If there are no unmarked paths, continue backtracking.²

You can cross that branch off because it has been completely explored and none of the paths leads to the exit. If all paths have been explored and there is no arrow, then either you didn't follow rule one correctly or you're back where you started and the maze is impossible. Oh dear, perhaps you can phone for help or something.

The String Method

Used by the Greek hero Theseus to find his way out of the Minotaur's maze, in this method you tie one end of a suitable length of string to something at the entrance, then reel it out as you go along. When you need to get out again, just follow the string.

This can only be used to find your way back to the entrance, but it does have the advantage over the left-hand method that you can explore any branches that take your fancy, giving you a better chance of reaching your goal. If you leave the string nice and loose, it will mark out everywhere you've been, so you can eliminate parts of the maze in a similar way to the marking method.

The Cheating Method

Buy a guide, map, or aerial photo, and mark the way through the maze with a pen. When you enter the maze all you need do is follow the path and find your way to the exit. You could also create your own map while exploring the maze. Most mazes are probably simple enough to be mapped with just pencil and paper, but a really complicated one with tunnels and stuff might require more sophisticated equipment, such as a compass or a theodolite.

The 'Randomly Wandering Around' Method

This is one of the most popular methods, and can be started from anywhere in the maze.

When you come to a junction, pick a path at random and follow it. Continue until you either find the exit or die (of exhaustion, dehydration, or sheer boredom).

Related BBC Links

• Why not See what BBCi has to say about mazes?

• Exercise your brain with more puzzles and mind-benders from BBCi Games.

Graphic supplied by Community Artist Clelba