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.)
(In reply to
re(4): About the by Cheradenine)
That's a huge assumption, and one that isn't justified by your problem. For one thing, the problem never stated that there was only one exit. For a large number of nodes, that exit can be arbitrarily far away from the starting node. However, the starting node is obviously very close to itself. I think it's reasonable that it then follows that the odds of reaching the starting node following some path are higher than those of reaching the exit. I haven't proved it satisfactorily, but I think it's true that every node is adjacent to at least one loop, but there is no guarantee that following any wall from a particular node will lead to the exit.
As n gets very large, I'd go so far as to venture that the odds of the starting node being completely surrounded by interior loops goes toward 1. I would tend to think of the maze as looking something like a Voronoi diagram with a boundary (A Voronoi diagram looks kind of like a bunch of soap bubbles stuck together on a 2D surface. A fairly decent representation I found on a Google search can be found here: http://eudoxus.usc.edu/SimplicialVIEW/Figures/voronoi.gif. Note that most of the vertices are completely surrounded by loops, so no wall following strategy will work at all. They only have a chance of working at nodes near the edge of the maze.
re(5): About the
