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 2-way maze (Posted on 2004-11-01)
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.

 Submitted by Tristan Rating: 4.0000 (4 votes) Solution: (Hide) ``` 3 2 3 2 3 1 │ □ □ □ □ 3 │ ┌─┐ □ □ 5 └─┘ │ ┌─┐ 3 □ □ └─┘ │ 1 □ □ □ □ │ 3 2 3 2 3 1 │ □ □ □ □ 3 │ □ ┌─┐ □ 5 └─┐ │ └─┐ 3 □ └─┘ □ │ 1 □ □ □ □ │``` So far, the answer is a 5 x 5 Invisible maze, and the sum of the numbers on the walls is 26.

 Subject Author Date Puzzle Thoughts K Sengupta 2023-06-30 07:57:12 computer verification of minimum Charlie 2013-08-18 14:31:49 re(4): A Try Richard 2004-11-03 21:54:51 Important clarification Tristan 2004-11-02 01:38:55 A minimalization from SteveH owl 2004-11-02 00:29:13 re(4): 4 X 4 Probably Min owl 2004-11-01 23:23:49 re(3): 4 X 4 Probably Min Juggler 2004-11-01 23:18:36 re(2): 4 X 4 Probably Min owl 2004-11-01 23:15:47 re(2): 4 X 4 Probably Min owl 2004-11-01 23:13:45 re: 4 X 4 Probably Min Juggler 2004-11-01 23:08:06 re(3): A Try SteveH 2004-11-01 23:07:38 re: 4 X 4 Probably Min SteveH 2004-11-01 22:56:34 re(2): A Try Richard 2004-11-01 22:55:17 re: 5 X 5 Paths owl 2004-11-01 22:51:29 re: A Try owl 2004-11-01 22:49:02 4 X 4 Probably Min owl 2004-11-01 22:47:59 5 X 5 Paths SteveH 2004-11-01 22:44:41 A Try Richard 2004-11-01 22:41:59 Clarification questions nikki 2004-11-01 18:12:51 7x7 non-minimized Jer 2004-11-01 17:55:53 Is this how it works? Dustin 2004-11-01 16:48:30

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