Solving mazes is more than following a few useful tips.
But tips are helpful anyway, so here are some more:
In general, when a maze crafter puts together a maze, he writes in the walls first, leaving open spaces to travel through. To go through a maze, then, the solver must dodge the walls all the way until they reach the finish. Usually, however, he will look at a maze and see (correctly) a collection of pathways that need to be followed –– something like a conglomeration of thick white ropes twined and packed together over a dark background. This leads to what might be considered a positive and optimistic focus. Seeing the maze this way, as he transverses through the maze, the solver will excitedly see every new path as another new possibility. Unfortunately for such cheerful souls, solving mazes is a splendid example of absolute truth: only one pathway is correct, and trying to see the good in all the surrounding ones, no matter how nice it sounds, does not help much in finding the goal.
Take this example:
Someone taking each and every path without suspicion will get tangled up in several places, such as the ones here marked 1 and 2.
This can be avoided if the solver knows beforehand which paths to check out and which to ignore. The secret is to focus not on following pathways, but on dodging walls. With this focus, the solver might have realized how useful it would be to follow the walls with his eyes, to see where they lead. Paying attention to where the walls go, the solver could have noticed trends like this, marked in blue and green:
Looking at this information, it is obvious that there is no way out of the green and blue areas. Many of the alluring pathways, it turns out, lead to systems of dead ends.
This tactic requires tracking along the walls with the eyes to see how far they extend, which takes practice. Still, it saves time in the end, especially if done in addition to the traditional method of testing individual pathways.
Besides quickly discovering hidden traps, like the green and blue ones, the trick of dodging walls can be used to give a general idea of where the final pathway can go. For example:
Here, the maze solver discovers he can trace a wall running from the top right edge almost all the way down to the bottom, making it clear the solution must run through one of the two paths indicated by the arrow. In this case, the maze solver can take the information and quickly find that both of those paths connect to start. Then, he only needs to find which one makes it all the way to Finish.
This usage builds off of a fundamental rule of mazes: for it to be possible to solve, a maze can never have a wall traceable from one edge of a maze all the way to the other (e.g. from top to bottom, if Start and Finish are on left and right). If it did, there would be an impenetrable barrier between Start and Finish and all pathways would eventually dead-end, as shown here:
In fact, this is a fundamental property of all unsolvable mazes –– technically even for those with bridges. They always have a traceable wall from one edge of the maze to the other.
The wall-tracing trick, unfortunately, cannot always be used effectively even on solvable mazes. For bridge mazes, made of woven pathways, it is of no use at all, because any pathway can lead to anywhere in the maze at all regardless of where the other pathways are. For other mazes, the walls are made to create complicated winding lines, in order to make following them with the eye very drawn-out and tiring. Often in the end for these it is more of a bother to trace walls than to check paths in the old-fashioned way. In these cases, tracing the walls can still help, but it takes much more work.
This maze should be excellent practice for the tips given here –– the walls are relatively easy to trace (though, conversely, the pathways are harder to follow!). Simply dodge all the messy lines and make you way to the bottom.
