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(5): Extreme stupidness by Angela)

Hi Angela, welcome to the debate.  You're right, the original problem doesn't require constructing the exit sequence.  But it does ask if such a sequence exists (I take "finite time" to mean a finite number of moves).  So if I can show how to build a finite-length escape sequence, I've demonstrated that God wins.

That's what we've done.

Posted by Ken Haley on 2005-02-16 05:41:55