## Mazes

© Copyright 2000, Jim Loy

Here is a simple maze. It is much simpler to solve this backwards. So you might want to solve it forwards.

Normally, it is easier to solve a maze backwards. The reason for this is that the designer of the maze has set traps for the normal solver, the one who solves mazes forwards. And some of these traps do not trap those who solve mazes backwards. For this reason, maze designers usually consider it cheating to solve mazes backwards.

The main reason why a maze is often more difficult in a forward direction is that the maze composer has probably placed decision points (marked with * in the diagram at the right) near the beginning of the maze, and not near the end. These are points in the maze where relatively difficult choices must be made. In my maze, there are no difficult decisions at all, if you solve the puzzle backwards. I assumed that you would start at the beginning, not the end.

Another clue is shown in the second diagram. I have darkened a continuous wall from the right side all the way to almost the left side. You cannot go through this continuous wall; so you must go around it, obviously to the left of it. That makes the solution very easy. This trick can simplify some very complicated mazes. You may have a continuous wall on the left that almost meets a continuous wall on the right, and the path then must go between these two walls.

One type of trap (one that is not easier backwards, by the way) is shown at the left. These are popular with maze designers, because they look like a dead end, at first glance. Of course, it is just a straight path, twisted into a double spiral. These can be bigger or circular (or of other shapes). If a maze contains a bigger version of this feature, then you should probably consider entering this area of the maze. The puzzle composer may have put it there because many people will assume that it is a dead end. But the composer may figure that you already know that.

There is an old bit of wisdom that many people know, that you can always solve a maze by keeping one hand on one wall, and traverse the maze that way. This way, you negotiate a dead end by merely by following the three walls, and then moving back the way you came. This works for most mazes. But, if the maze has a central blank area, which is occupied by a second maze, this technique does not work. Also, for mazes with some three-dimensional aspects (paths that go over other paths), this trick may (rarely) be too simplistic. This method amounts to what is known in graph theory as a depth first tree search.