## Solve mazes by starting at the exit

It worked on this one.

Good maze designers know this trick and are careful to design multiple branches in each direction. Back when I was in junior high, I used to make huge mazes, and the basic idea was to anticipate what the solver might try to do and to make the maze difficult by postponing the point at which he would realize a path was going nowhere. For example, you might have 6 branches: one dead end, two pairs that form loops going back to the start, and one that is the correct solution. You do this from both directions and add some twists and turns, and there you are.

But the maze designer aiming for the naive solver–the sap who starts from the entrance and goes toward the exit–can simplify matters by just having 6 branches: five dead ends and one winner. This sort of thing is easy to solve in the reverse direction. I’m surprised the Times didn’t do better for their special puzzle issue.

1. Jerzy says:

I always love hearing about an entire field of work/art, like maze design, that I've never really thought about.

I lost interest in doing mazes as a kid after I heard about the wall-following approach (like the mathematician who says "a solution exists"). It seemed like — where's the fun in solving a maze if you know you can just brute-force it?

But (1) I just realized that wall-following only works if all the walls are connected — things like loops and separations can mess you up… and (2) regardless it's great that people can still have fun solving mazes by trying to be clever about it, coming up with heuristics that might work faster than wall-following, and designers can have fun by trying to outwit clever solvers.

Did you have friends who were into mazes too, and take turns making/solving each other's mazes? Or did you make them just for your own amusement?

2. xi'an says:

I first read solving mazes by staying at the exit!

3. Fernando says:

I must be old fashioned but I thought starting at exit was considered cheatin :-)