Aw, that's easy!
Actually, it wasn't all that easy... it took me a lot longer than I thought it would. I thought I'd have it nailed in under an hour, but it took me closer to two. Then again, I'm not very clever
Dude, your map is imperfect. I can't really use exact grid stuff with it!
Yep, I ran into the same problem, though I didn't use any grid stuff. Because of the way it's drawn, I had some trouble with occasionally getting stuck because if my computer hiccuped then Mr. Mouse would drop frames and time-delta inside a wall. With a better designed maze this could be avoided pretty easily.
Anyway, I think I have it all sorted out now. At least, the last three times I ran the maze Mr. Mouse got the cheese just fine.
Download: http://www.box.net/shared/8p4iv3i27e
I used 8 Direction (with the controls shut off, of course). The rules for the mouse are as follows:
1. If there is an open path to the right, he turns right.
2. If he hits a wall, he will attempt to turn right.
3. If he can't turn right, he will turn left.
4. If he can't turn right or left, he will turn around and go back the way he came (this is a last resort).
It takes him a while to get the cheese, but he gets there eventually. My method is kind of crude, but hey... it works. I'm sure someone else could come up with a much more elegant and streamlined solution.
Like I said he might still get stuck occasionally. If so, just restart the game.