Now that Splinter’s cool “Maze Challenge” is complete, I thought I would throw out another maze challenge. This challenge involves my new 3D rolling ball maze puzzles; “Ethereal Maze Puzzles”. They are a newly invented type of 3D maze there and are no documented techniques that you can use to help solve this type of maze. So the challenge is to come up with some practical methods that can be used to help solve these new type of mazes.

An example of a technique is one used to help solve a Garden Maze, where you walk through a maze made of hedges. One widely known practical technique is to walk through this 2D maze always following the wall on the left side. You will eventually come out the exit.

My newly invented 3D maze are called “Ethereal Maze Puzzles”. You solve these maze puzzles by inserting the ball into the entrance, and then roll the ball through the 3D maze to try to reach the exit. The directions the ball can move through the maze are up, down, left, right, towards you, or away from you. When you reach the exit there is a spring button that releases the ball when pressed. So far there are 5 different models of Ethereal Maze Puzzles. Two of these have just been released as of January 27, 2012 (“Twisted Symmetry” and “Minotaur’s Castle”). Next some information to get you started on the challenge:

All the dead-ends in the mazes are very short, mostly one or two turns. You know you are at a dead-end if there is only one way for the ball to go from there; up, down, left, right, towards you, or away from you. After backing out of the dead-end you will soon be at a junction on the main path, but which way should you go? It is easy to be turned around at that point and not be sure of which way you came from. If you could figure out a method that would help you determine that you were not traveling in the wrong direction, then you would be able to make good progress towards the exit. Can you figure out a way to do that? Or can you think of some practical methods to help solve these puzzles?
Post your ideas on practical ways to solve this new type of maze here. Maybe you will be the first to come up with a totally new 3D maze solving technique.

You can get a good look at the internal structure of these mazes in the videos of them I have posted at my Shapeways shop, and on my Youtube channel. Check them out and let me know what you think.

http://www.shapeways.com/shops/EtherealMazePuzzles

My Youtube and Facebook Ethereal Maze Puzzles pages below:

http://www.youtube.com/user/EtherealMazePuzzles
http://www.facebook.com/pages/Ethereal- ... 11?sk=wall

Good Luck with this new Challenge!

PS: Below is one of my latest Puzzles; “Minotaur’s Castle”. It is the same size as a Rubik’s Cube.

Funny that you mention techniques now; I just yesterday made a new technique for your 7x7x7 Ethereal maze:

I grabbed a shoe string, and leaded that through the maze. Like old Perseus with the Minotaur
I think I now have the solution for the 7x7x7 maze, but will check it by having the ball follow the string while pulling the string out (I can better see the string and the route from it, than with only a ball that is jumpy. But I like the puzzle very much)

I only have no mathematical solution yet, but the 'trial and error method' (and looking carefully).
I'm anxious to learn what people come up with for your challenge....

Wow, can you post a photo with a string going through the maze. That would be very interesting to see!

One problem that I can see with using string is that with this new type of maze there are not always complete side walls to the maze pathways. For example when the ball is in a cell inside the maze it may be prevented from moving right by a wall, but one that is only half as high as the ball. But if you are pulling a string through the maze it could easily go into the next cell to the right, where the ball can't go. Do you have any ideas to address that?

Thanks for getting the "ball rolling" on this challenge.

Here's how I came to the solution for the 7x7x7. I've to tell honestly that when pulling the string out and having the ball follow, I saw I made a mistake in the route of the string: I made a shortcut the ball couldn't take. But also here the string helped me to see 'the extra loop' to get back on the correct track.

My conclusion: it's difficult to lead the string through the maze (also because its studs are rough and not polished), but it definitely helps you see where you went and where you want to lead the ball.
And it shows how nice Steve has almost used all edges and turns in the cube to create the route
(the 7x7x7 is certainly not easy to solve 'in a glance', as you have to turn the cube to be able to direct the ball. And then the chance of losing sight of the correct route is huge....)

Thanks to Splinter for the photos of his method of using string to help map out a route through the maze. These gives you a good visual on how convoluted the pathways through the maze are.

I think we are off to a good start on this challenge. As Splinter concluded his string method can be very difficult. Lets see if others can come up with some simpler techniques that can be used to help solve the maze. To help I will provide some additional information on the mazes that may not be obvious from examining them. Hopefully these will get some more ideas going.

1 – There are no mathematical formulas that you would need to solve the mazes. The pathways are created much like those for a 2D maze, but with 3D the pathways in these mazes they can have some additional properties. One is that one section of a path can wrap completely around another section. Another property is that one section of a path can partially overlap with another section, but the ball can’t go between these overlapping sections.

2 – The maze pathways were not designed with any one side of the maze being “up”. So don’t be afraid to rotate the maze every which way in order to roll the ball through the pathways. This does make it easy to loose track of where you came from in the maze, which is one of the aspects that makes these 3D mazes so challenging and fun.

3 – When rolling the ball from one cell to an adjacent cell there sometimes is a rail along the middle of the “floor” going in the direction to roll the ball. In this case the ball will roll smoothly along that path, and it is easy to control. If there is not such a rail on the “floor” then this can make a little dip that the ball will drop into. When that happens you will need to tip the maze a little to get it past the dip, and roll into the adjacent cell. This makes it more difficult to control the ball, particularly if the ball is at a branch in the pathway where there is a dead-end to get past. In this case you can look for a smoother route. Look at the side walls of the cell the ball is in. Maybe there is a rail along one of those wall that extends in the direction towards the adjacent cell the ball is to go to next. If that is the case you can rotate the maze so that wall is now the floor. Now you can roll the ball smoothly to the adjacent cell.

Keep those ideas coming.

I'd just guess there would be some inventive software programmer here, that can come up with a nice script to solve such mazes with a kind of routine.

At least mathematically I see some boundaries:

- the width, height and length of the cube are known (can be expressed in e.g. max. 7 paths wide/high/long)

- the gate for a path should be at least have value '1' for the ball to pass

When knowing / taking into account such boundaries, one can at least determine that in a 7x7x7 maze a path never can be longer than 7 steps straight forward, straight backward, straigth upward etc.

I wonder what routine can be programmed to efficiently solve such mazes; e.g. something like

<go forward> if not possible then <go ..... >
<if possible> then continu <go forward>

maybe also implementing some 3-D 'right hand (or left hand) rule' (wander like a kind of cork-screw as a basis?).


Just some thoughts. (I'm obviously no programmer)

The simplest solution is to assign a fixed orientation to the maze (i.e., one side is designated "up", the opposite side is designated "down", and the four remaining sides designated "north", "south", "east", "west"), and then assign a fixed order to the directions, for example, U,D,N,S,E,W. Then you just recursively try all combinations, backtracking when you get stuck. To prevent getting stuck in loops, you can store a "visited" attribute to each position in the maze. Something like this:



This works for mazes of any dimension, not just 2D and 3D.

EDIT: of course, while this algorithm will find a solution, it may not be the best solution if there are multiple paths through the maze. For that, you'd want something like Dijkstra's algorithm. But the maze traversal (recursion based on trying each direction in a fixed order) remains the same.

Now, that's what I meant by a script! Great!

Well Steve, just run the script in your maze at the PC and you can see whether it works

(or try it out with a marker for the spots already visited with the ball in the real maze)

Actually, that's no script, that's just pseudo-code. To actually turn it into something that can be run will take a little more work.

these mazes are awesome

definitely my favourite kind of maze

these will definitely be on my "to purchase" list

Here's a video of me solving "Escher's Playground" on YouTube. We'd like to see the times people could possibly get. If you could, post a video of you solving "Escher's Playground" and post it as a responce to this post or to my YouTube video here:

http://www.youtube.com/watch?v=pZG5FgK55kE

My fastest time currently is 46.87 seconds. Could you guys beat that?

Good luck!

Wow, that is a really fast time. Much faster than I can do it. I think you are the current World Champion on "Escher's Playground"! Very nice video, I will keep an eye on your Youtube channel to see if anyone can beat your time.

Congratulations!