You're trapped in a maze. There is a way out. Path junctions are all 3-way.

If you use the strategy of always taking the path going right, what will happen?

(Note: This problem is deliberarely vague.)

Perhaps what you want to see is the theory worked from inside the maze.

From where you are, there is a "best" way out of the maze, but you don't know what it is, so you follow the right hand strategy. If the first turn of the "best" path is to the right, you are going the right way, if it was to turn left, you are going the wrong way.

Assume for the moment, that all wrong turnings eventually lead to a dead end. Also assume that this one dead-ends immediately. You turn around and return to the junction. At this point, the dead end is behind you, your starting point is to your left, and if you follow the the right-hand strategy, you will take the (correct) path that had been on the left the last time you were in this junction.

If the (wrong) right-hand path branches before it dead-ends, you will wind up tracing out each of those wrong brances before arriving back at the "critical" junction, but the situation once you get there is exactly the same.

The same thing happens every time the "best" path would have been to turn left, and eventually you find yourself at the exit.

But remember, this was based on the assumption that all wrong turnings eventually dead-end. This is the same as saying there are only outside pieces of the maze. It is also possible for the wrong turnings to eventually lead you in a circle and that you wind up back where you started. Once it does that, following the right-hand strategy will just keep you retracing the same paths. The wall on your right is completely inside the circle you are tracing. It is an inside piece.

Posted by TomM on 2002-06-26 07:22:44