God and the Devil decide to play a game. God will start by picking an infinite sequence of moves of the form "left", "right", "up", and "down". The Devil responds by creating a finite maze with an exit and by placing God somewhere inside. God then follows His pre-selected sequence to traverse the maze. Unmakable moves are ignored; for example, if the next move is "left" and there is a wall to the left of the current square, God goes on to the next move in the sequence without moving.
If God escapes the maze in finite time, He wins. Otherwise, the Devil wins.
Assuming both agents act optimally, who will win?
(assume that the maze is formed by deleting some edges from a rectangular grid, and that it has no isolated regions; i.e., it is always possible to get to the exit from any point inside the maze)
(In reply to re(2): Clarification of infinite sequence
David Shin wasn't bashing on anybody, and you should not have called him a pompous twit.
I noticed in your profile that you rated one problem, and you voted 1. Since your only comment was on this problem, I am led to believe that the problem you rated as 'horrible' was this one. Did you really think the problem was horrible? Or were you venting your frustration with David Shin on his problem?
Posted by Dustin
on 2005-02-09 22:38:13