An Invisible Maze is a square room with a tiled floor, in which the tiles form a grid. You may walk only to adjacent tiles (no diagonal moves). There is a number on the wall for each row and column of tiles. An Invisible Maze can have any numbers on the walls provided that it has at least one True Path. A True Path will take you from the northwest corner to the southeast corner, and the number of tiles you touch in each row and column is equal to the corresponding number on the wall.

There is an NxN tiled Invisible maze that has at least two different True Paths. Minimize N and then, using that N, minimize the sum of all the numbers on the wall.

Important: Two paths are considered the same even if they touch the exact same tiles in a different order.

(In reply to re: A Try by owl)

"Nice try, but I think the Important Note is aimed at preventing this one. Does it?"

I don't really know. My thinking though was that the two paths are NW NE SW and NW SW SE, which don't touch exactly the same tiles in a different order. I haven't read the other solutions yet, so maybe they will be more clearly what was intended.

Posted by Richard on 2004-11-01 22:55:17