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(3): Solution attempt - Jack was right by SteveH)

The only problem is that God doesn't know the layout of the maze when God chooses God's sequence of moves.  How does God know how to get out from A, or B, or anyplace?

I hate to keep shooting down ideas, but I have none of my own.

From what it sounds like, the Devil gets to look at God's list of moves, and then try to create a maze to keep God in forever.

Is this correct?

Posted by Dustin on 2005-02-09 01:54:34