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 Post subject: Re: Puzzles that jumble
PostPosted: Sat Jul 03, 2010 8:24 pm 
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Ok... I've rotated the puzzle as a whole and I'm now looking down a cut plane (which I've made twice as wide as before) and turned the background blue. So if the puzzle could turn along this cut plane you'd be able to see blue along its whole length. You can't because there are interior pieces blocking it. And now as I look at it myself there are pieces besides the central shallow cut helicopter cube that block the rotation.

Attachment:
Puzzle4.png
Puzzle4.png [ 126.73 KiB | Viewed 7387 times ]


Here check out the piece on the right... I'll move the view over to that cut plane.

Attachment:
Puzzle5.png
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See all the pieces blocking this rotation? You could take the central shallow cut helicopter cube out and replace it with a void and it still wouldn't work.

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Sat Jul 03, 2010 8:32 pm 
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And one last picture before I call it quits for today.

Attachment:
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Look through your monitor off into infinity. The two images will form a 3rd in between them and its in 3D. Check it out... if you can.

I call this the poor man's 3D glasses method.

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Sat Jul 03, 2010 11:34 pm 
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What program is this?

Also I am proven wrong. However, I still think my logic is correct. So that brings up the question could a non fudged mixup cube rotate in this fashion without getting blocked?

The problem I had with seeing this was my version of the puzzle does not have those moves blocked. Thanks for all the help trying to show me why I was wrong :D

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 Post subject: Re: Puzzles that jumble
PostPosted: Sun Jul 04, 2010 12:46 am 
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wwwmwww wrote:
Look through your monitor off into infinity. The two images will form a 3rd in between them and its in 3D. Check it out... if you can.

Maybe it's just me, but I find it's easier if the images are switched and you just go cross-eyed.
Attachment:
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PuzzleMaster6262 wrote:
What program is this?

He uses POV-Ray. You need to write scripts to build the models, it doesn't naturally do crazy twisty puzzle things. It's an incredibly powerful program and it's a bit like using a steamroller to get toothpaste out of a tube for wwwmwww's usage, but it gets the job done and they do have nice shading afterwards.

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 Post subject: Re: Puzzles that jumble
PostPosted: Sun Jul 04, 2010 1:05 am 
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Someone should start a new thread, puzzles in 3d :lol:

Thank you for the program name.

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 Post subject: Re: Puzzles that jumble
PostPosted: Sun Jul 04, 2010 11:44 am 
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PuzzleMaster6262 wrote:
However, I still think my logic is correct. So that brings up the question could a non fudged mixup cube rotate in this fashion without getting blocked?


Yes, you could simply have the Mixup Cube. I don't consider it fudged but I'd be tempted to call it a Twisty/Slidey Puzzle.

PuzzleMaster6262 wrote:
The problem I had with seeing this was my version of the puzzle does not have those moves blocked.


Could we see your version? It sounds to me like you have the Mixup Cube.

PuzzleMaster6262 wrote:
Thanks for all the help trying to show me why I was wrong :D


Your welcome,
Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Sun Jul 04, 2010 11:59 am 
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I will be 3d printing my version soon so you can see it then :D

What I was saying about the mixup cube was if it was built without sliding parts, would it have the same internal bandaging as the other puzzle

We need a name for the other puzzle so that it isn't just called the other puzzle :lol:

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 Post subject: Re: Puzzles that jumble
PostPosted: Sun Jul 04, 2010 12:02 pm 
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GuiltyBystander wrote:
He uses POV-Ray. You need to write scripts to build the models, it doesn't naturally do crazy twisty puzzle things. It's an incredibly powerful program and it's a bit like using a steamroller to get toothpaste out of a tube for wwwmwww's usage, but it gets the job done and they do have nice shading afterwards.


Its just the only 3D modeling program I know how to use. Its free and I taught myself how to use it oh about 7 or 8 years ago during a period while I was unemployed for about 6 months. I haven't had the time to learn any other programs since. That and I use it for other things besides Twisty Puzzles.

Attachment:
Sidecar.png
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And the sidecar can also take off on its own. It doesn't need a set of wheels. ;)

Attachment:
Flyer.png
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I've seen TRON mentioned here before so I thought a few here might enjoy these.

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Sun Jul 04, 2010 12:09 pm 
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I use blender(also free) and it works great at cgi but making puzzles with it is a pain. A new version of Blender is being made that hopefully will make it better.

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 Post subject: Re: Puzzles that jumble
PostPosted: Sun Jul 04, 2010 12:15 pm 
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PuzzleMaster6262 wrote:
I will be 3d printing my version soon so you can see it then :D


Cool. I'm eager to see it.

PuzzleMaster6262 wrote:
What I was saying about the mixup cube was if it was built without sliding parts, would it have the same internal bandaging as the other puzzle


I'm inclined to say yes but PLEASE prove me wrong. The universe gets broken around these parts ALL the time.

PuzzleMaster6262 wrote:
We need a name for the other puzzle so that it isn't just called the other puzzle :lol:


Agreed... I ended up resorting to calling it "the new truncated rhombic dodecahedron jumbling puzzle" a few posts ago but that is FAR from the best name for it. How about Mixup Wannabe.

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 Post subject: Re: Puzzles that jumble
PostPosted: Sun Jul 04, 2010 12:53 pm 
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wwwmwww wrote:
Agreed... I ended up resorting to calling it "the new truncated rhombic dodecahedron jumbling puzzle" a few posts ago but that is FAR from the best name for it. How about Mixup Wannabe.

Carl

Atleast for now I think that's a great name for it :mrgreen:

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 12:17 am 
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I've been playing with the idea of jumbling sliding puzzles and I think I've come up with a few puzzles that are a little more interesting than that 3 tile example. Both of these puzzles involve taking two sliding puzzles and combining them so that they can't interfere with each other and unbandaging them will never completely separate them.

The first method rotates one puzzle and place it on top of the other. This way, the slides of 1 on one puzzle are slides of 1/sqrt(2) in the other puzzle.

The second method is to scale one of the puzzles up so that it's tile size is irrational compared to the other. The tiny red piece is there just to stabalize the puzzle while you're working on the green part of the puzzle.
Attachment:
IrrationalTiles.png
IrrationalTiles.png [ 3.73 KiB | Viewed 7296 times ]


I imagine the state space something like this. I think it feels a bit like cheating because there's very few crossover states, possibly only 1. But I guess this is almost like the fused cube except that you're forced to only work on one at a time.
Attachment:
statespace.png
statespace.png [ 8.67 KiB | Viewed 7296 times ]


Other than at the cross-over points, I can't think of many ways this puzzle can jumble besides this simple example below. I don't see it having much use though atm besides just adding a tad more difficulty to the solve. And by tad, I mean like the trivial corners on a tetrahedron. Unbandaging might add a tad more as well.
Attachment:
tinyjumble.png
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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 12:32 am 
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If you build one of those puzzles, I'll have to add slide jumbling as a subgroup :D

That is a really cool idea and could open up a whole new world of sliding puzzles.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 9:11 am 
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GuiltyBystander wrote:
Attachment:
tinyjumble.png


What do the colors of the arrows mean? I'm a bit confused.

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 9:40 am 
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It means you can swap the two pieces on either end of the arrow. Here's how to switch them. You'll see that the original green puzzle will continue to function normally, but the blue puzzle will now act bandaged.
Attachment:
tinyjumble2.png
tinyjumble2.png [ 6.57 KiB | Viewed 7265 times ]


Re-reading your question, I see you're asking what the colors mean, not the arrows. It just shows the distinction of which puzzle you're jumbling. I guess I probably should have used green/blue arrows. I'll leave the pic above incase someone else finds it useful.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 9:51 am 
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And here is another question that I think fits in this topic. Consider this puzzle.

Is Smart Alex a bandaged pure twisty puzzle? Or a 1x1x2 with slidey parts? Is it both? If it can be unbandaged into a pure twisty puzzle what does it look like?

What about the Cheeseblock seen here:
http://twistypuzzles.com/forum/viewtopic.php?f=15&t=9762

This can be unbandaged into a doctrinaire puzzle. Its the Pipe Connector seen here:
http://www.twistypuzzles.com/forum/viewtopic.php?f=15&t=14075

But again... are these Twisty/Slidey puzzles? Could they be considered bandaged versions of a "pure" twisty puzzle?

However we'd classify these puzzles I'd call the Pipe Connector and Vergo's 2x2 seen here the exact same puzzle.
http://mypuzzlestop.com/Vergo-s-Cube.html

Another bandaged version of this doctrinaire puzzle is this one:
Image

I'm not sure of its name. But I know the Square 1 can be thought of as a bandaged pure twisty puzzle... so can these?

I'm not sure,
Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 10:04 am 
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I think all except the square 1 thing are unbandaged puzzles like the mixup and fused cube.
The pipe puzzle I think does not slide while the vergo cube does. :?: :?: :?:
Also I love the cheeseblock :D

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 10:10 am 
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GuiltyBystander wrote:
Re-reading your question, I see you're asking what the colors mean, not the arrows. It just shows the distinction of which puzzle you're jumbling. I guess I probably should have used green/blue arrows. I'll leave the pic above incase someone else finds it useful.


Ahh... That helps alot. Thanks. Is the red box in the top right needed? I'm not sure if that is intended to show space that pieces can move into or just that the green pieces aren't free to move into the top right corner and rotate for example. I'm thinking it means there is a L shaped piece present when the green pieces are moved that isn't there when the blue pieces are moved. Correct?

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 10:39 am 
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PuzzleMaster6262 wrote:
I think all except the square 1 thing are unbandaged puzzles like the mixup and fused cube.

Well maybe we aren't even starting on the same page. I consider the Square 1 a bandaged "pure" twisty puzzle. It can be unbandaged with a finite number of cuts into a doctrinaire pure twisty puzzle.

The Mixup Cube is a doctrinaire puzzle. If it were in the shape of a Rhombicuboctahedron without stickers then the puzzle would look exactly the same before and after a turn (Twist or Slide). However I don't consider this a pure twisty puzzle as discussed above. I'd say its a Twisty/Slidey puzzle.

The Fused Cube is a doctrinaire puzzle. Again take all the stickers off and the puzzle and it looks exactly the same before and after a twist. Its a pure twisty puzzle and is a subset of the 3x3x3.

That said... I believe the Smart Alex is a doctrinaire puzzle. If you take the stickers off all states of this puzzle look exactly the same. But is it a pure twisty puzzle or is it a twisty/slidey puzzle?

The Cheeseblock is NOT a doctrinaire puzzle. Take the stickers off and turn one of the set of 6 pie shaped pieces by 30 degrees and the puzzle looks different. It's bandaged. It can be unbandaged by cutting the 6 pie pieces into 12 and that is exactly what is done with the Pipe Connector which is a doctrinaire puzzle but is either a pure twisty puzzle?

PuzzleMaster6262 wrote:
The pipe puzzle I think does not slide while the vergo cube does. :?: :?: :?: .

To me the Vergo Cube is a shape mod of the Pipe Connector. The pie shaped pieces have just been turned into spheres. If one is a pure twisty puzzle I'd say both are. If one can be proven to be a twisty/slidey puzzle I'd say they both are.

PuzzleMaster6262 wrote:
Also I love the cheeseblock :D

I agree with you there. They are all great puzzles

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 11:28 am 
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wwwmwww wrote:
I'm thinking it means there is a L shaped piece present when the green pieces are moved that isn't there when the blue pieces are moved. Correct?

Yep. I didn't want a giant gaping hole there when you're working on the smaller tiles. I think I miscolored it too. The L shape thing should be a light grey instead of the hole color because it is an actual piece. And no, it's not strictly necessary.


With regards to the Pipe, Vergos and the Square-1 varient, I see them all as being part of the same class of puzzles as the Fractal Cube which I'm guessing you don't see as a pure twisty puzzle. There's clearly a well defined hierarchical order to all of them.

I'm not completely sure what it is you want to see in a "pure" twisty puzzle. Here's a couple ideas that ran through my head. Take them or leave them.
  • The axis of all rotations go through the origin. I was thinking about disqualifying the fractal cube and the Knob Cube for this.
  • You can take the cuts on the puzzle and apply them to a solid of infinite size and still have a functioning puzzle and it's behavior is well defined. This is a take on your multicube idea.


Speaking of the Knob Cube, that would be an interesting puzzle to see unbandage. I think you'd end up with something like this on each of the 3x3x3 faces. I think there's 65 pieces on each of the 3x3x3's faces.
Attachment:
KnobUnbandaged.png
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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 11:44 am 
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GuiltyBystander wrote:
Attachment:
KnobUnbandaged.png


Off-topic, but I think that would make an awesome 2-D twisty puzzle, and would be even better mounted to the faces of a cube.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 12:00 pm 
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The square 1 thing could be made into a square 2 thing. That's why I had excluded it from being unbandaged. I now agree about the cheeseblock also being bandaged. With the other two, I agree that they are the same but the one with spheres just looks like a slide puzzle but that would mean a 2x2x4 can slide :?: :?: :?:

How would my 4x4x4 with "Super Edges!" fit into this idea of pure twisty puzzles? By just changing the shape, it can be bandaged and unbandaged yet all axes of rotation go through the center.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 1:55 pm 
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GuiltyBystander wrote:
With regards to the Pipe, Vergos and the Square-1 varient, I see them all as being part of the same class of puzzles as the Fractal Cube which I'm guessing you don't see as a pure twisty puzzle. There's clearly a well defined hierarchical order to all of them.

I'm not completely sure what it is you want to see in a "pure" twisty puzzle. Here's a couple ideas that ran through my head. Take them or leave them.
  • The axis of all rotations go through the origin. I was thinking about disqualifying the fractal cube and the Knob Cube for this.
  • You can take the cuts on the puzzle and apply them to a solid of infinite size and still have a functioning puzzle and it's behavior is well defined. This is a take on your multicube idea.


I view the Fractal Cube and Knob Cube as siamese twisty puzzles. The Fractal cube is formed of a bunch of 1x2x2 pure twizy puzzles all siamesed (is that a word?) together. The Knob Cube is a 3x3x3 with a 2x2x2 siamesed onto each face. So I don't think of their moves as slidey moves but yes they aren't really PURE twisty puzzles either. Note both the Fractal Cube and the Knob Cube allow pieces to move between puzzles. One 2x2x2 cubie on the Knob Cube can move from one 2x2x2 to another. Similiar to the way like sized pieces are moved between 1x2x2 puzzles on the Fractal Cube. Not all siamese puzzles have this property.

So I guess when I see puzzles where all the axes of rotations don't pass through a common point I break them up into a merger of seperate puzzles that do have that property.

I guess I'd define a pure twisty puzzle as:

(1) A puzzle formed from a finite set of cut planes (or surfaces) that pass entirely through the puzzle. These cut planes (or surfaces) allow rotation about an axis that passes through the center of the puzzle.

(2) Any puzzle that can be considered a subset of a puzzle fitting definition (1). Fused Cube is an example.

(3) Any puzzle that is mathematically equivalent to a puzzle fitting definition (1). The normal Circle 3x3x3 is an example.

You can think of a puzzle like the Circle 3x3x3 that is formed of planar cuts and cylindrical cuts that pass completely through a cube and all cuts allow rotation about axes that pass through the center. However this puzzle isn't a normal Circle 3x3x3 as it allows the circle centers to rotate freely of the middle layer. You can bandage this puzzle into a normal Circle 3x3x3 by fixing all face centers to the core but I don't view the Circle 3x3x3 as bandaged as its equivalent to a 3x3x3 with Super Stickers that show the face center orientation.

In that light I guess you could call this puzzle:
Image
The merger of of 3 seperate Square 1 puzzles. All 3 can share pieces with each other. However as all 3 DO share a common point where all the axes of rotation meet, I'm curious if it could somehow be unbandaged into one puzzle that would fall into definition (2) above?

GuiltyBystander wrote:
Speaking of the Knob Cube, that would be an interesting puzzle to see unbandage. I think you'd end up with something like this on each of the 3x3x3 faces. I think there's 65 pieces on each of the 3x3x3's faces.
Attachment:
KnobUnbandaged.png


9 green pieces
32 blue pieces
24 yellow pieces
8 red pieces

I get 73 pieces counting the exposed 3x3x3 faces themselves. And yes that would be one very interesting puzzle. I don't think I could call that a siamese puzzle either as you are creating pieces that aren't 2x2x2 pieces and they aren't 3x3x3 pieces either.

Carl

P.S. The above definition is for 3D puzzles. For 2D twisty puzzles, the axes of rotation need to be parallel and perpendicular to the surface of the 2D puzzle. Or you could think of them as existing on the surface of an infinite sphere were you are just looking at a subset of some infinite 3D puzzle. This does allow the axes to still share a common point. With this in mind I guess I'd call your proposed puzzle a siamese puzzle of a 2x2x2 and six 2D pure twisty puzzles, one on each face.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 05, 2010 3:04 pm 
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PuzzleMaster6262 wrote:
With the other two, I agree that they are the same but the one with spheres just looks like a slide puzzle but that would mean a 2x2x4 can slide :?: :?: :?:


No a 2x2x4 is a pure twisty puzzle. See the definition I posted. It fits (1) and it could also fall into (2) as a subset of a Multi-4x4x4.

PuzzleMaster6262 wrote:
How would my 4x4x4 with "Super Edges!" fit into this idea of pure twisty puzzles? By just changing the shape, it can be bandaged and unbandaged yet all axes of rotation go through the center.


Well it could be looked as as a 4x4x4 with 12 2x2x2's siamesed to the edges. The axes of rotation all pass through the center though so maybe it could be a bandaged version of a puzzle that would fall under definition (2) above.

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jul 06, 2010 10:22 am 
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I agree about my puzzle.

What I was saying about the 2x2x4 was it doesn't slide but could be made from what looks like a sliding puzzle.
A definition of sliding is needed so that exactly every normal puzzle either slides or doesn't slide.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jul 06, 2010 7:06 pm 
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wwwmwww wrote:
I view the Fractal Cube and Knob Cube as siamese twisty puzzles. The Fractal cube is formed of a bunch of 1x2x2 pure twizy puzzles all siamesed (is that a word?) together. The Knob Cube is a 3x3x3 with a 2x2x2 siamesed onto each face.

To me, the key feature (and disappointment) of a siamese puzzle is that it's 2 or more puzzles that are connected, but moves on one puzzle do not affect the pieces of the other. For that reason, I wouldn't say that the fractal, knob, and siamese cubes are in the same class.

I guess there's always a million ways to look as a puzzles and I just see siamese different than you. By your definition, the cross-cube could be a siamese cube made of 7 2x2x2. It could also be seen as a corner-less and edge-less 4x4x4.


wwwmwww wrote:
I get 73 pieces counting the exposed 3x3x3 faces themselves.

I was just counting the "knob" pieces, but yes your counts were what I got too.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jul 06, 2010 7:33 pm 
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GuiltyBystander wrote:
To me, the key feature (and disappointment) of a siamese puzzle is that it's 2 or more puzzles that are connected, but moves on one puzzle do not affect the pieces of the other. For that reason, I wouldn't say that the fractal, knob, and siamese cubes are in the same class.


Maybe Siamese is used for the murger of two puzzles that don't share pieces and we can come up with another word for the murger of two puzzles that do. I would be ok with that. Maybe conjoined puzzles.

GuiltyBystander wrote:
I guess there's always a million ways to look as a puzzles and I just see siamese different than you. By your definition, the cross-cube could be a siamese cube made of 7 2x2x2. It could also be seen as a corner-less and edge-less 4x4x4.


I also try to fit puzzles puzzle in the most basic class they will fit into. Yes you could view a cross cube as 7 conjoined 2x2x2's but its not needed. Its a pure twisty puzzle all its own. It fits definitions (1) and (2) above as is. So I wouldn't call it a conjoined puzzle.

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jul 06, 2010 8:00 pm 
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PuzzleMaster6262 wrote:
What I was saying about the 2x2x4 was it doesn't slide but could be made from what looks like a sliding puzzle.
A definition of sliding is needed so that exactly every normal puzzle either slides or doesn't slide.


A good definition of sliding will depend on a good definition of fudging if they aren't considered the same. If you group the two together you might be able to say that any twisty puzzle that isn't "pure", i.e. fits the definition above, contains either slide or fudge moves assuming its considered unbandaged. And then you need a really good definition of bandaged. To me bandaging is more then just glueing pieces together, its any restriction placed on the puzzle. I consider the Gear Cube a bandaged 3x3x3 for example.

And if I'm going to talk of twisty puzzles and "pure" twisty puzzles I also need to define what I call a twisty puzzle. Using what I have above I'd start here:

Twisty Puzzle is:

(1) A puzzle formed from a finite OR INFINITE set of cut planes (or surfaces) that pass entirely through the puzzle. These cut planes (or surfaces) allow rotation about an axis that passes through the center of the puzzle.

(2) Any puzzle that can be considered a subset of a puzzle fitting definition (1). Example the Mixup Cube.

(3) Any puzzle that is mathematically equivalent to a puzzle fitting definition (1)

(4) Any puzzle formed by siameseing two or more puzzles together that fit definition (1)

(5) Any puzzle formed by conjoining two or more puzzles together that fit definition (1)

(6) Any puzzle containing a void, which if filled, would fit definition (1). Example Polo Cube by ALEX and OSKAR.

(7) Any puzzle formed by bandaging any puzzle that fits any of the definitions above.

I tend to think (4) and (5) maybe should read:

(4) Any puzzle formed by siameseing two or more puzzles together that fit definition (1) and have different centers of rotation.

(5) Any puzzle formed by conjoinging two or more puzzles together that fit definition (1) and have different centers of rotation.

As any puzzle that does just have one center of rotation I think would (or could) fall under definitions (1), (2), or (3) and not be considered siamese or conjoined.

Note the puzzle inside a Polo Cube (not sure of its name) isn't a twisty puzzle by itself as there is no rotation allowed. It's a pure slidey puzzle.

Carl



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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jul 06, 2010 8:12 pm 
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Sliding and fudging are different things. Sliding is how the pieces move while fudging is how the puzzle is made. My definition of fudging is the addition of voids within a mechanism allowing pieces to move in additional ways. A definition of sliding could be moving pieces along a path without a central point or moving into a void.

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 Post subject: Re: Puzzles that jumble
PostPosted: Wed Jul 07, 2010 4:59 pm 
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Actually I think we need to subgroup sliding :lol:

Sliding movemnet-motion of pieces along a path without a center point or moving along a path into a void.

Sliding mechanism-pieces sliding along a track with unfilled voids allowing movement that would be impossible without such voids, real or imaginary.

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 Post subject: Re: Puzzles that jumble
PostPosted: Wed Jul 07, 2010 8:04 pm 
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Ok... thanks to Andreas's thread on the Supergroup of the SeniorBarrel I now see how to deal with puzzle like these:

Smart Alex
Cheeseblock
Pipe Connector
And what ever this is called:
Image

I wasn't sure they were pure twisty puzzles or twisty slidey puzzles. However using this definition:

Pure Twisty Puzzle:

(1) A puzzle formed from a finite set of cut planes (or surfaces) that pass entirely through the puzzle. These cut planes (or surfaces) allow rotation about an axis that passes through the center of the puzzle.

(2) Any puzzle that can be considered a subset of a puzzle fitting definition (1). Fused Cube is an example.

I can now see ALL these puzzles are just that... PURE twisty puzzles as they are all subsets of this solid cut with 21 cut planes.

Attachment:
Pipe.png
Pipe.png [ 170.36 KiB | Viewed 7091 times ]


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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 08, 2010 6:06 pm 
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I just wanted to share an interesting little tidbit of info I recently discovered:

Oskar's Fairly Twisted puzzle jumbles at, among a few other angles, exactly 120 degrees, which is a rational number last time I checked :wink: This is the first physically constructed puzzle that I am comfortable calling jumbleable that does jumble at a rational number. The other angles are irrational however.

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 08, 2010 6:24 pm 
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Allagem wrote:
Oskar's Fairly Twisted puzzle jumbles at, among a few other angles, exactly 120 degrees
Incorrect!

(Edit: sorry, Matt is right!)

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Last edited by Oskar on Fri Jul 09, 2010 7:26 am, edited 1 time in total.

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 08, 2010 6:42 pm 
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Oskar wrote:
Allagem wrote:
Oskar's Fairly Twisted puzzle jumbles at, among a few other angles, exactly 120 degrees
Incorrect!

Are you sure? :?: I realize that this is not the ONLY angle but as near as I can tell this marked angle is exactly 120 degrees:
Attachment:
FairlyTwisted120Degrees.png
FairlyTwisted120Degrees.png [ 38.62 KiB | Viewed 7054 times ]

There is one such angle on all 7 turning faces. So rotating any face in 120 degrees either direction will allow one of these two groups of pieces to replace the other in all cases right? Hence a jumbling move of exactly 120 degrees. Yes?
well I realize this doesn't exactly hold true for one face, but that face is very unconventional for many reasons

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 Post subject: Re: Puzzles that jumble
PostPosted: Fri Jul 09, 2010 7:25 am 
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Allagem wrote:
Oskar wrote:
Allagem wrote:
Oskar's Fairly Twisted puzzle jumbles at, among a few other angles, exactly 120 degrees
Incorrect!
Are you sure? I realize that this is not the ONLY angle but as near as I can tell this marked angle is exactly 120 degrees
Matt,

I stand corrected, you are right. My 3D model measures 120.00 degrees at this angle. Wow, how unexpected! How did you discover this? Is there any geometric logic why this should be exactly 120 degrees?

Oskar

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 Post subject: Re: Puzzles that jumble
PostPosted: Sat Jul 10, 2010 10:38 am 
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What about the Canny Uncube and the Uncanny Cube? From the videos of them, I can't tell if they jumble.

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 Post subject: Re: Puzzles that jumble
PostPosted: Sat Jul 10, 2010 11:53 am 
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PuzzleMaster6262 wrote:
What about the Canny Uncube and the Uncanny Cube? From the videos of them, I can't tell if they jumble.


I believe both puzzles jumble. To keep it from jumbling you have to remove the interference between the faces.

You could call this the Non-Jumbling Canny Uncube if you wanted to.

Image

Picture from gingervergo's post here:
http://twistypuzzles.com/forum/viewtopic.php?p=218733#p218733

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 Post subject: Re: Puzzles that jumble
PostPosted: Sat Jul 10, 2010 12:07 pm 
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so then that adds two puzzles with rational jumbling, any more?

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 Post subject: Re: Puzzles that jumble
PostPosted: Sat Jul 10, 2010 7:02 pm 
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The Canny Cubes unbandages to a shallower cut version of the 2x2x2 + Partial Helicopter Cube. Shallower on the 2x2x2 side so that part is a 3x3x3. I can't quite visualize the jumbling part, but if it's related to the 2x2x2 + Partial Helicopter Cube, then it's almost defiantly jumbling right?
Here's a pic I drew so I could see the first stage of unbandaging on the top.
Attachment:
cannycubes.png
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 Post subject: Re: Puzzles that jumble
PostPosted: Sat Jul 10, 2010 7:50 pm 
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Rotate any side 90 degrees.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Oct 18, 2011 1:56 pm 
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How about the Dayan Gem I and II?

And it would be nice to keep a list below the main one of mass produced puzzles that jumble.
I think it would it be:

Helicopter Cube
Curvy Copter
Helicopter Dodecahedron
Dayan Gem I
Dayan Gem II

am I missing any?


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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 09, 2012 3:27 am 
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I've updated the list with what I could find but it is still missing a lot of puzzles and a lot of details. If you have made a jumbling puzzle please help out and calculate its jumble angle. Hopefully Carl and other members can use this list to better classify jumbling and its sub sets.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jul 09, 2012 5:40 am 
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Objection!

Diamond Delight, TriTangle, Twin TriTangle, Sunrise Sunset and Ice-9 do not jumble. Tsk tsk.

Also, you're missing the Bermuda cubes. (rational jumbling, 45 degrees)

In my opinion the Tuttminx (with curved cuts) should be included aswell. It can jumble, whether it was meant to or not.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jul 10, 2012 1:56 am 
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Coaster1235 wrote:
Objection!

Diamond Delight, TriTangle, Twin TriTangle, Sunrise Sunset and Ice-9 do not jumble. Tsk tsk.

Also, you're missing the Bermuda cubes. (rational jumbling, 45 degrees)

In my opinion the Tuttminx (with curved cuts) should be included aswell. It can jumble, whether it was meant to or not.

Thank you! I just went through David's shop and added everything.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jul 10, 2012 2:23 am 
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Coaster1235 wrote:
In my opinion the Tuttminx (with curved cuts) should be included as well. It can jumble, whether it was meant to or not.
I am afraid that your opinion does not match with Bram Cohen's definition of jumbling. Tuttminx is a doctrinaire puzzle that has 12 faces with five-fold symmetry and 20 faces with three-fold symmetry. It would only jumble if you would make at least one additional cut. But that statement is also true for a regular Rubik's Cube.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jul 10, 2012 2:50 am 
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Oskar wrote:
Coaster1235 wrote:
In my opinion the Tuttminx (with curved cuts) should be included as well. It can jumble, whether it was meant to or not.
I am afraid that your opinion does not match with Bram Cohen's definition of jumbling. Tuttminx is a doctrinaire puzzle that has 12 faces with five-fold symmetry and 20 faces with three-fold symmetry. It would only jumble if you would make at least one additional cut. But that statement is also true for a regular Rubik's Cube.

Oskar

The mass produced tuttminx can rotate like your futtminx. If we think of it as fudged, it can jumble. So should we say a partially fudged tuttminx jumbles?

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jul 10, 2012 3:12 am 
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I don't think the Futtminx should be considered jumbling and neither should the MP Tuttminx. Strictly speaking, the MP Tuttminx would be jumbling: if you take the exact cuts and turning options you get a jumbling puzzle (probably, though I'm not sure). The Futtminx has been fudged to "remove" jumbling and as such, is truly not jumbling. However, because the MP Tuttminx allows illegal moves it implements exactly the same puzzle as the Futtminx and should not be considered to jumble.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jul 10, 2012 3:28 am 
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PuzzleMaster6262 wrote:
The mass produced tuttminx can rotate like your futtminx. If we think of it as fudged, it can jumble. So should we say a partially fudged tuttminx jumbles?
No, see Tom's response.

Here is my design challenge to you: make a Muttminx (Mike's Tuttminx). Muttminx has the same number of pieces and the geometry of a Tuttminx. All moves are either fluent or blocked, no ambiguous jamming allowed. And unlike Tuttminx or Futtminx, Muttminx has to jumble according to Bram's definition.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jul 10, 2012 4:07 am 
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I understand now. The fudging to allow 60 degree rotations is also enough to make any jumbling in-effective at blocking rotations. I've removed it from the list.

But your design challange is tempting. Possible or not it will help me understand the puzzle.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jul 10, 2012 5:32 am 
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PuzzleMaster6262 wrote:
Undefined
Pascal's Jumble 1 & 2:Rational Jumbling?
Pregnant Prism:Irrational Jumbling?
More Madness
Crazy Comet
Fairly Twisted
Meteor Madness

More Madness, Pregnant Prism, Crazy Comet and Meteor Madness: all irrational jumbling
Failly Twisted and Fairly Fudged: mixed rational + irrational jumbling (Carl discovered a viable 120-degrees jumbling turn).

Oskar

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