There is debate as to whether Carl Banks, creator of Scrooge McDuck, or Christopher Thomas originally coined the following phrase.
Work smarter, not harder.
Regardless of the author, it seems a good quote to keep in mind on Labor Day, and I was reminded of it when my sons were solving mazes yesterday. I thought they might enjoy learning a little theory that would make solving a maze easier, now that they’ve gotten quite good at completing mazes with brute force.
Before sharing with you what I shared with them, here are two maze-related jokes.
The first is a maze for liberal arts majors, who always seem to have trouble finding their way.
The second is a maze I call Good Frickin’ Luck.
With those out of the way, on to the theory of mazes.
For simply connected mazes — that is, those mazes for which every wall is connected to either another wall or to the boundary — solving the maze can be accomplished by coloring the walls with just two colors. That’s because such mazes consist of two disjoint parts, and the solution path lies between those two parts.
Consider the simple maze below, which, by the way, I created “on the spot” for my sons when they had completed all the mazes in their activity books.
You can then color all of the connected walls on the top half of the maze red, and you can color the other walls blue. This gives the following result, and the solution is the path that lies between the red and blue halves, as shown.
My kids thought that was pretty cool. Hope you did, too!