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 Post subject: Switched Maze by OSKAR
PostPosted: Sat Mar 02, 2013 10:49 am 
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Hi Non-Twisty Puzzles fans,

Switched Maze is a mechanical maze. The object is to roll the metal ball from "Start" to "Goal". The ball is impeded by gates at several points in the maze. By rolling the ball against the levers, gates can be opened and closed.

This maze is related to Robert Abbott's Sliding Door Maze and Eldon Vaughn's Amaze. The rules of Abbott's puzzle is electronically enforced by the software implementation. The rules of Vaughn's maze is psychologically enforced by the game rule that says not to lift the stylus from the board. The switched Maze is fully mechanically enforced. That is, you cannot cheat without taking the puzzle apart or removing the transparent cover.

Switched Maze implements logical one-way gates, logical crossings and a Chinese-Rings type of passing point. Most likely, one could build a Turing Machine using the Switched Maze concept.

Watch the YouTube video.
Buy the puzzle at my Shapeways Shop.
Read more at the Shapeways Forum.
Check out the photos below.

Enjoy!

Oskar
Attachment:
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Switched-Maze-v2---view-1.jpg [ 36.79 KiB | Viewed 2344 times ]

Attachment:
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Switched-Maze-v2---view-2.jpg [ 27.92 KiB | Viewed 2344 times ]

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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Sat Mar 02, 2013 11:21 am 
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It is a nice implementation, but the maze is too easy. ;)


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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Sat Mar 02, 2013 11:37 am 
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Jared wrote:
It is a nice implementation, but the maze is too easy. ;)
That is a rather bold statement for someone who hasn't even tried it. I can tell you that several people tried and failed at a recent local puzzlers event.

Oskar

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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Sat Mar 02, 2013 11:54 am 
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That's awesome! Great job.

-Doug

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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Sat Mar 02, 2013 1:33 pm 
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It is indeed a very nice puzzle, Oskar. :D

Oskar wrote:
Jared wrote:
It is a nice implementation, but the maze is too easy. ;)
That is a rather bold statement for someone who hasn't even tried it. I can tell you that several people tried and failed at a recent local puzzlers event.
Oskar
Starting with the state of the puzzle at the beginning of your video, one needs to make only 11 operations of reversing the state of particular switches in a specific order (to go from IN to OUT). So, not taking into consideration the dexterity aspect, I would agree with Jared that this is a fairly easy version. :wink:

I bet there could be a way to make it very difficult (like Panex is to Hanoi).

Peace,

Skarabajo.

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Last edited by Skarabajo on Sat Mar 02, 2013 1:42 pm, edited 1 time in total.

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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Sat Mar 02, 2013 1:41 pm 
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Oskar wrote:
Most likely, one could build a Turing Machine using the Switched Maze concept.

I think this is probably right, at least a space-bounded Turing machine. This puzzle ought to be PSPACE-complete. I'm looking at it.

I'm impressed that you could make a challenging puzzle with only three switches!


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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Sat Mar 02, 2013 2:58 pm 
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Oskar wrote:
Jared wrote:
It is a nice implementation, but the maze is too easy. ;)
That is a rather bold statement for someone who hasn't even tried it. I can tell you that several people tried and failed at a recent local puzzlers event.

Oskar


In fact I was able to solve the maze in my head. I'm pretty sure I didn't mess up either: the order of switches after the ball is at the point pictured above is blue, blue, red, blue, green, blue, red, blue, and then you can get out, right? Along with the three switches to get to that point (red, red, green) that makes the 11 that Skarabajo confirmed.


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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Sat Mar 02, 2013 5:45 pm 
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bhearn wrote:
Oskar wrote:
Most likely, one could build a Turing Machine using the Switched Maze concept.

I think this is probably right, at least a space-bounded Turing machine. This puzzle ought to be PSPACE-complete. I'm looking at it.

OK, yeah, I have the gadgets built in my head. I haven't written them down, but I'm pretty confident they work. This type of switch maze is PSPACE-complete, like sliding-block puzzles, Rush Hour, Sokoban, and many others, but unlike ordinary mazes.


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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Sun Mar 03, 2013 6:06 am 
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Jared wrote:
In fact I was able to solve the maze in my head. I'm pretty sure I didn't mess up either: the order of switches after the ball is at the point pictured above is blue, blue, red, blue, green, blue, red, blue, and then you can get out, right? Along with the three switches to get to that point (red, red, green) that makes the 11 that Skarabajo confirmed.
Excellent, I am impressed, congratulations! As this challenge is apparently too easy for you, here is a harder one: "design a harder Switched Maze on the same grid size".

Enjoy!

Oskar

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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Sun Mar 03, 2013 1:41 pm 
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Hmm, I've never designed a logic maze before, so I wouldn't know where to begin... Can you have two sets of perpendicular switches in a physical version, or would there be unfortunate lockups?

I think something interesting would be to find some way to combine this with the Irreversible Cube's mechanism for switch blocking.


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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Tue Mar 05, 2013 3:17 am 
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When you look at the internal parts of this puzzle at Shapeways, I think the mechanics of it are rather intriguing.

And it's a maze of course, so it's by definition interesting ;-)

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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Tue Mar 05, 2013 11:07 am 
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I've been looking forward to this for a while. It looks great!

So, building a Turing machine from this concept, eh? Designing extremely basic and abstract computers is my forte! The only real "issue" that I can see is designating how the ball must move, but using binary switches for a rules table sounds like a great idea. Now the question is if the rules table should be a 4-tuple or 5-tuple. 4-tuple seems easier to implement, but it would require a much larger rules table. Actually, I don't even know if it it's even POSSIBLE to make a 5-tuple rules table with this. I could definitely see 4-tuple working. What do you guys think?

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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Tue Mar 05, 2013 5:13 pm 
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Jorbs3210 wrote:
So, building a Turing machine from this concept, eh? Designing extremely basic and abstract computers is my forte! The only real "issue" that I can see is designating how the ball must move, but using binary switches for a rules table sounds like a great idea. Now the question is if the rules table should be a 4-tuple or 5-tuple. 4-tuple seems easier to implement, but it would require a much larger rules table. Actually, I don't even know if it it's even POSSIBLE to make a 5-tuple rules table with this. I could definitely see 4-tuple working. What do you guys think?

As I posted above, the construction already exists -- in my head. I'm pretty sure it works. I did my Ph.D. on games, puzzles, and computation.

It is an indirect reduction, so you wouldn't see explicit Turing machine mechanics in my construction. But if you are interested I can try to make some figures of the necessary gadgets.

The reduction is polynomial-space-bounded Turing machine acceptance -> Quantified Boolean Formulas -> Nondeterministic Constraint Logic -> Switched Maze. What this means is that, if you give me a (polynomial-space-bounded) Turing machine and an input, I can give you back a Switched Maze, such that the maze is solvable if and only if the Turing machine accepts the input. So effectively, it embodies the identical computation.

Step 2 of this reduction chain (QBF -> NCL) was part of my Ph.D. thesis; step 3 (NCL -> Switched Maze) is what's in my head.

An explicit Turing machine construction would be fascinating as well, however, though significantly more complicated. Most of the work in proving the result has already been done in showing that NCL is PSPACE-hard.

A more interesting question here is, which elements of Switched Maze gadgetry are actually necessary to show PSPACE-hardness (effectively, to build a computer)? My reduction is simplified by the fact that switches can have multiple levers and multiple pairs of blocking arms. Is it still hard if we tighten these restrictions? One pair of blocking arms (or maybe just a single blocking arm), one lever? I don't know. The gadgets I came up with wouldn't work.


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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Wed Mar 13, 2013 10:07 pm 
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It looks like a very fun puzzle, such a simple design. I wish i had one! :D

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Last edited by TimmyCuber98 on Thu Mar 14, 2013 2:03 pm, edited 1 time in total.

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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Thu Mar 14, 2013 3:14 am 
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Oskar wrote:
Excellent, I am impressed, congratulations! As this challenge is apparently too easy for you, here is a harder one

You should probably cut the sarcasm.


Also, if many people say the challenge is easy, it has nothing do do with your design, but with the solving, and I agree with them, you can figure out the way to go in your head quite easily. It's implementing that solution that can be tricky for example if the ball doesn't go the right way when you want it to.

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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Thu Mar 14, 2013 10:54 am 
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RubixFreakGreg wrote:
You should probably cut the sarcasm.
I hate it when people interpret a sincere compliment as sarcasm. Not many people can correctly solve such puzzle in their mind. I was impressed, especially as correctness evidence was included.

Oskar

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 Post subject: Re: Switched Maze by OSKAR
PostPosted: Thu Mar 14, 2013 1:13 pm 
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I didn't read your comment as a sarcasm in the first place.
I got a bit uncertain when I read Greg's post and I'm really glad that you clarified this.

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