To the untrained eye, a maze will look like an incoherent jumble of paths. This is not an accurate way of seeing these puzzles, however; mazes may contain a bonanza of unique, defined sections with different qualities, all of which confuse and misdirect the unwary mind.
Last month’s article began to follow the process I took when sketching a maze, commenting on the different aspects of it from the maze crafter’s point of view. This will pick up where it left off.
There have been several additions since last month. (A) is a complicated path drawn without attachments to either Start or Finish. For now, the maze crafter does not know if this path will include the solution or lead to a dead end, or anything else about it. It gives another aspect for him to work with later when he ties up all the loose ends, and helps ensure complexity without requiring too much time and effort. At (B), the maze maker has added another loop for later use, this time with a dead end attached to it. Finally, (C) shows a line curving the opposite direction than would be expected for a path drawn out from Finish. This avoids the problem maze crafters sometimes have of constructing the maze so that the correct path is clearly defined and easy to follow with the eye. By making the path harder to follow with the eye, this technique makes the time to solve the maze a little longer, especially if the solver does not watch out for it.
Whew! A lot has been added here. Most of it, however, is straightforward: (A) is a long extension of a disconnected loop (i.e. a loop not connected to Start or Finish), while (B) and (C) contain numerous paths branching out in complicated directions –– used, again, to confuse the solver. (D) –– separate from (C) here –– exhibits a new technique: graining. Basically, the maze crafter has stacked several paths on top of each other, giving the maze a grain, like wood. This befuddles the solver by encouraging the eye to scan from left to right, instead of from top to bottom, thereby directing the eye away from the solution. (D) also has a lot of branching, including one six-way intersection. That could cause problems later on.
Here, (B) and (C) show simple extending and branching, respectively, but (A) shows something new –– looping. This differs from other types of “looping,” which refer to simple curves in the paths. It is the alternative to a dead end in a maze, the method of bending paths back to connect to their starting point, so that the solver could, theoretically, start moving in circles. In this case, this conveniently connects some of the many branches from the lower left. Thankfully for solvers, this kind of loop often appears in the most confusing parts of mazes. An intersection rife with branches is often used to overwhelm the solver’s poor brain and freeze them in indecision. All those extra paths need to go somewhere, though, and usually creating loops is the simplest way to efficiently complete them. In that case, the solver might not have to search out every path after all!
Now, a little later, the new additions mostly consist of simple branching and extending of pathways, but a significant number are becoming dead ends. Ultimately, this is because of a lack of space –– if he could, any maze crafter would love to send his false trails to the moon and back. (A), (B), and (C) show some examples of this. Start forks into three pathways. (A) shows the final dead ends of one of these. This makes it the first complete dead end in the maze –– every option leads to a blank wall. For the solver, finding a complete dead end is always a major accomplishment, narrowing the options.
This maze is nearing completion, so the maze crafter can easily sum up many of its distinct sections. By carefully examining his maze, he can observe the effects of the different loops and lines on his paper, and decide on the final connections, deciding which parts to utilize and which to ignore for the final solution. Accordingly, here is my summary of this maze, presented as The Maze Map:
Key:
Light Blue –– empty spaces which still need to be filled in. These are what the maze crafter is primarily looking at.
Light Purple –– numbers noting the possible spaces the paths from Start and Finish might arrive at. The complete dead end, of course, goes Nowhere.
Barren Wasteland –– this is the area that I, as the maze crafter, want all my victims to go to. Anyone who goes there will wander in circles never to be seen again.
Dead End Alley –– a large area with a curiously high proportion of dead ends. (The name, by the way, is supposed to be like Tornado Alley, not like little back roads between buildings). There are also Isolated Outbreaks of Dead Ends farther down.
Dark Blue, also known as the Trampoline Bounce –– the innocent puzzle-solver skips to the edge of the cliff and giddily jumps down toward the finish… before suffering the terrible disappointment of the Trampoline Bounce, sending him right back where he came from.
Now, with all these parts clearly understood, here is the completed maze:
I have certainly given you plenty of help for solving this one!
