Solving a Maze

Eleanor Roosevelt Community Learning Center (ERCLC) is a charter school serving homeschooling families. From time to time I teach a class at ERCLC for younger students called "Math Explorations." (I describe it as "stuff that doesn't look like math.) The maze solution came out of one session in which I simply passed out some big complicated-looking mazes and we all worked on our mazes looking for and sharing strategies as we came across them. One strategy I tried was tracing a wall from the center of the maze to see which outer wall it connected to. That had the effect of eliminating large portions of the maze from consideration. This led to the insight that all the walls were connected in two groups separated by the solution path. I ended up solving my maze by the method shown here with crayons. A lot of work! I then realized this could be done on a computer with a flood-fill command using any paint program.

Extensions:
--Why did I paint twice? Why not just paint once and let the colors be red or black? The maze shown here is simply connected. in other words all the walls connect to one side or the other. Some mazes are multiply connected, so there are islands. Try this method with such mazes (or create multiply connected mazes by painting out a wall or two on a maze like this.)

--I tried using this method on a circular maze where the goal was to get from the outside to the center. In this case ALL of the walls are connected into one group, so the method will not work. Look for a way to modify the technique to work on that kind of maze.

This lesson led to other lessons where we created our own mazes. Try it.

Category:

Education

Tags:

• education

[MathFourVideos]

Brilliant! I love it!