Those who make mazes know the inner workings of mazes like the backs of their hands. It is natural for them, since putting the maze together requires thinking and understanding of the situation but does not come naturally to the solver. In my own experience, I learned more new secrets about the workings of mazes –– and how to use those secrets for solving them –– from practice in making mazes, rather than practice in solving them. With this in mind, I will, over the next two articles, present and comment on the process I took in making a particular maze –– and if you aspire to make mazes, it will help you too.
Maze crafters do not start all their mazes in the same way. I have started mazes from doodling interesting patterns, and then built off of that in all directions. In general, though, it is best for the maze crafter to start with an outline, to keep the maze looking neat. As the outer boundary, the outline forces everything to yield, so that all paths, upon arrival at the border, must either dead end, switch direction, or travel alongside it. In addition to the outline, I have added the start and finish, which the paths of the maze work out from.
Now, a little later, the start and finish are entirely enclosed, and the pathways leading out from them have been established, pointing in different directions –– four for Start, and three for Finish.
Here the development of the paths includes lengthening them (A) –– not in a straight line, which is easy to follow with the eye, but all crooked –– and branching them out (B, C). (C) is an example of a conventional intersection, of one path splitting into two others, at which point the solver must choose between two equally appealing pathways. (B) is a broken wall intersection, where two parallel paths have a break in the wall between them, ultimately adding up to a unique four-way intersection. Because the eye will naturally follow along a path pointing in the original direction, this type of intersection is especially hazardous for the solver, as the more alluring paths can distract from the correct one. At (E) is a new addition made separate from the original paths from Start and Finish, and at (D) is another, specifically a planned dead end. Planned use of empty spaces this way tends to make a maze more complex, with paths connecting to each other in unexpected patterns.
Uh oh, warning! (A) is an example of treading on dangerous ground for a maze crafter, as the intersection points anyone coming from Finish directly at Start, making the other path useless. In this case it might be justified because the path from there to Start is smooth and easy and would probably be found in any case, but it is still dangerous. The solver should not rely on having his eyes lead to the solution this way most of the time, though –– very often, the maze maker will manipulate the paths to direct attention away from the correct point; so the solver must always be aware and careful to check all paths. (B) shows a rather involved example of extending a planned dead end, and branching it off extensively (I got carried away). (C) shows a zigzag –– a section of path which switches direction twice and greatly slows up the eye following it, more effectively than any other methods which take up similar space. This is why so many of the dead ends seen in this maze end with a small turn –– at first glance, it is not evident that the path ends in a dead end, and the solver can be induced to waste time by following the path all the way to the end. The dead end attached to (B) is not very well done; here it functions primarily as a space filler. At first glance the repeated pattern seen in (D) would appear to be only a space filler as well, but such repeated curves do keep the eye from following the path as easily, unless the eye is already prepared to look for, and follow, staggered curves like this. Skipping through a pattern automatically can, with practice, speed up the maze-solving process. Why not save as much time as possible? Patience is essential to solving mazes, but for those who must work hard to attain it (like me), little tricks like this add up to ease the burden.
At one point I had thought I had lost the following old maze of mine, but I was mistaken. I later discovered it doing service as my mom’s bookmark. I was very happy –– it’s one of my favorites:
All images by the author.