Euler suggested that any solvable maze can be solved by going along the wall of the maze(citation needed). Now he doesn't make such a suggestion out of the blue right.There has to be a proof. So it got me wondering if something can be so simple and if I can synthesize a proof. Then I went along and started thinking as I rode back home. Even though this was a long time back , the idea still is very fresh in my mind thanks to its simplicity. Now, the idea may be obvious once I present to you the essence of the proof. But a mathematical proof is necessary, just to put an end to any further discussions.
Now the first assumption is that the maze is solvable. So, going against the obvious, let us construct a simple solvable maze. Two non intersecting lines from region A to region B ( not necessarily straight) with a path leading from region A to B. Once this is done we are twist and turn these two lines like a thread to make many topologically similar shapes. Here these two lines can be stretched indefinitely and compressed indefinitely . The many topologically similar structures are nothing but the mazes that we see in the newspapers every day. Traversing the wall amounts to tracing one of the morphed yet topologically similar lines from A to B. Since the such a line is bound to reach B, traversing along it results in arriving a the destination no matter what.
Will soon come forward with a java applet to describe the post visually so don't be disappointed if you aren't convinced. Have a great day.
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