perplexus.info :: General : 2-way maze

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.

Comments: ( You must be logged in to post comments.)

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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