# Create a changeable maze

I have quite a creative task with many, but a bit vague limitations. Can someone help me with it?

One needs to create a 2D cell-based maze, like this one:

The criteria:

1. The solution should be not trivial for a person who is inside the maze. (The partitions are walls, higher than human hight.)
For example this maze is trivial, there is only one side path and you can investigate it even without walking - just look and see the dead end there:

2. The size is in-between 6x5 and 6x10. Lesser size - better.

3. You can change it to 14-20 other mazes (non-trivial and significantly different) by moving N or less wall fragments (of size 1). Lesser N - better.

4. The length of the shortest path between entry and exit should be the same in all mazes.

5. Harder to solve each maze - better:

5.1. More non-trivial circling paths - better.

5.2. More non-trivial side paths (dead ends) - better.

Any ideas (even unfinished) and help is appreciated.

P.S. Many people seems to misunderstand what I mean by 2D cell-based maze. I mean that you take rectangular piece of squared paper with 6xM cells inside, and draw only along the lines (cells borders). The drawings will be the walls, and the rest will be the voice space the solver can walk through. Exactly like 2 mentioned examples shown.

• Are you looking for mazes, or criteria? Jun 23 '17 at 8:00
• I am not sure what you are asking for, but what I can say for sure is that for someone inside the maze, looping paths will be a million times more efficient than dead ends. The fewer the dead ends, the better, because they can be used to orient yourself. Also the more change of direction your loop has, the better. Jun 23 '17 at 8:06
• @Ankoganit, for mazes of course. Jun 23 '17 at 8:19
• Interesting question,but a tad vague. I'll assume you actually want to BUILD these for an event? Thus being able to vary without moving too much around being a plus? Jun 23 '17 at 11:22
• If I'm understanding sites.math.rutgers.edu/~zeilberg/tokhniot/oKamaEtzim1 correctly, there are 74795194705 acyclic maze layouts for a 6x5 grid, so if anyone was thinking of generating all of them and then filtering then they should change their strategy. Jun 23 '17 at 18:02

How about a puzzle piece style maze?

Break the 6x6 base into six 3x2 sections. Along the borders of these sections create permanent walls. Having permanent walls allows you to reduce the triviality of the maze and also removes the restrictions of the pieces having to align properly.

Then create 6+ puzzle pieces such that you can get from any one square to another (ie. 2 of the possible 7 walls are filled and they do not block off a corner). Make sure that the border walls of the pieces are completely empty, the permanent base walls act as the walls between the pieces.

Here is an example:

### Pros:

• $$8!/2! = 20160$$ possibilities
• $$N = 2, 4, 6, ... = \{2z | z \in {\bf Z}\}$$

### Cons:

• You would need added restrictions to ensure the minimum distance is the same for every maze
• Most of the dead ends will be trivial
• If the user figures out the pattern of the permanent walls, it will be much easier for them to navigate any randomly generated maze

Overall I think the concept has potential, but it definitely needs work. Perhaps you could make the maze 6x9 or 6x12 which would allow for 3x3 pieces, or maybe you don't need to follow a grid system at all.

I hope this helps! It would be cool if you posted your final result; I am curious to see what you come up with.

EDIT: Updated Example

• 6X6
• Any combination of the pieces will be 15 squares long
• Given any 2 pieces for C, $$2^4 = 16$$ combinations
• It is a first valid idea, ty, but the mazes like this would have 0 loops and 0 nontrivial deadends, if I'm not mistaken. Jun 29 '17 at 14:24
• @klm123 In the example I gave, yes. Again I would suggest using 3x3 pieces to allow for loops and meaningful deadends (at the cost of increasing N). You could also use different setups of the permanent walls such that certain rooms only have one entrance and hence the entire room is a deadend. Jun 29 '17 at 14:37
• Can you actually complete the answer and provide a set of mazes with solutions of equal length? This is the best answer so far, but it doesn't satisfy even the formal bounty conditions. :( Jul 2 '17 at 15:26
• Edited my answer to include valid solution. Jul 4 '17 at 13:44

(sorry for the poor graphic)

I think circular mazes are a bit trickier relative to their sizes. It's also harder to see if something is a dead end.

To build this I would first put enough centrifugal walls to make a separation between entrance area and exit area, add the doors for the correct path and then add more doors and walls to make it confusing.

step 1:

step 2:

step 3:

• Imagine a piece of squared paper, you are allowed to build walls only on the lines of this paper... Jul 1 '17 at 10:10
• This idea could still work if you used squares inside squares instead of circles. The corners would mess up the counting though. Jul 4 '17 at 13:50

Here is a maze I just thought up.

Green is the entrance,
Red is the exit,
Yellow are walls.
It is a very loopy maze that can make you walk the same path many times which will make it feel longer and bigger than it really is.
It is symmetrical enough so that it's hard to recognize specific patterns and make "landmarks". But it is also asymmetrical enough to confuse you and make you loose sense of direction.
The entrance offer you 4 paths right away which will "intimidate" the... "prisoner(?)" right away.
The exit is blocked with 2 walls to reduce chances of random successes.
It is also very customizable in case you want to change the pattern a few times during your event and give a new experience to the participants. You only have to make 4-5 movable walls and change their positions once in a while. Almost anywhere you put them will not make it impossible to solve.
You said you wanted a maze as small as possible, so I am not sure if mine is too big or not... but I think it's 6X6(?).

• So where are walls? all white are the walls? It is not 2D cell-based maze. At least, I have know how to reformulate it as 6x6 2D cell-based maze. If you don't know what I mean - imagine a 6x6 piece of paper, you are allowed to draw only along the lines. And what you draw (along those lines) will be the walls. The rest is the void space, which solver can explore/walk through. Jun 26 '17 at 7:45