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 4 X 4 Probably Min by owl)

Nice solution! I was trying to avoid repeated tiles, since I wasn't sure of the rules (whether they were 1. allowed and 2. counted again for each touch). But I think your approach fits the problem correctly, as worded.

Posted by SteveH on 2004-11-01 22:56:34