It would appear it is. I met Oskar van Deventer today so that I could give him a prototype I built him. The prototype was for a 'jumbling' puzzle. We wondered about what caused jumbling, so I pulled out my helicopter cube. Oskar's initial reaction was to get a screwdriver and disassemble it.

Then, after playing around with jumbling for a bit, he came upon this situation:


From this position, you are able to move the green marked layers, but not the one marked red. Oskar suggested (after another look at the mechanism): 'What if you modified the "triangular" piece a bit so you would be able to turn the layer?'.

I really liked the idea, so when I got home I tried doing this out. And the results are stunning:



On the left: normal triangle piece
Middle left: split up triangle piece
Middle right: exploded split triangle piece parts
Right: now that's the stunning part...

At the right, you can see one of the pieces of our old triangle piece superimposed on a corner piece. Now what can we see. Yes, it is exactly the same! The corner piece is a shape modification of the new triangle piece! They are mechanically identical!

The helicopter cube is a bandaged puzzle and by our current definitions, we would not regard the Meffert's bandaged cube as jumbling. Therefor, the helicopter cube does not jumble either! It is simply changing shape.

All this time, we have been seperating puzzles into two vague categories. Jumbling and shape-changing. And now we find that they are in fact the same. So all those times I have corrected someone, I was wrong.

©opyright 2009 Tom van der Zanden - You are not allowed to use this design at this time

Gra! I don't have time to lay this out properly, so I'll just put in my 2 cents for the moment and say that I *think* you've missed a feature about "jumbling" in that if you consider the swapped bits as bandged, it doesn't quite work as it implies the existance of additional (unused) rotational layers. Thus, "jumbling" does not equate to bandaging. I'll try and put together a clear-er explanation a little later.

Then again, I could be wrong too

Cheers!

Well yes, but you're not finished yet. By doing what you stated above you attempted to "unbandage" the helicopter cube right? well this creates new cuts (where there used to be "bandages") that also have to be considered. These new cuts should allow another point in the middle of a given move where a new jumble move can occur along the new cut. But by your definition that means the jumble move suggested the existence of another bandaged part of the puzzle, which you can find easily enough.

But then the pattern starts over again!!!!!!! Everytime you unbandage more of the puzzle you find a new jumble move that locates a new bandage and this pattern will never end because a jumbling move is not a factor of 360 degrees.

Look into this topic for more info:
http://twistypuzzles.com/forum/viewtopic.php?f=1&t=11126&hilit=jumble
especially wwwmwww's post with pictures about halfway down

Sorry to burst your bubble!!!

Peace

I never thought that the Helicopter cube was jumleable since not all of the pieces are the same. Here are my definitions

Jumble-A puzzle with only one type of piece that can change shape (i.e. 24/Little Chop)
Shape Changing- A puzzle with more than one type of piece that changes shape (Container, Mastermorphix)

No, jumbling does NOT equal shape changing.

Though I haven't been able to come up with exact definitions, the closest I can get is this: If the angle of rotation is irrational, it is jumbling and not bandaged. Unfortunately, as wwwmwww proved here, there are jumbling moves which are rational as well. So I suppose this comes to the not-so-good definition of: If the angle of rotation is irrational, it is jumbling and not bandaged. If it is rational, it may or may not be jumbling.

I would say what causes a puzzle to be shape changing (which I define simply as any puzzle that changes shape, jumbling puzzles included) is the platonic solid that it is. If all puzzles were spheres, none would be shape changing.

By my definitions, I would say that jumbling = shape changing. However, the real question you were asking is, does jumbling = bandaging? The answer to which is no.

The difference between jumbling and bandaging is that when you 'unbandage' a bandaged puzzle the process eventually terminates, but when you 'unbandage' a jumble puzzle the puzzle eventually turns into dust and you still aren't done unbandaging it. But that doesn't mean that the unbandaged puzzles are uninteresting! The slightly unbandaged helicopter cube you describe, for example, would probably be quite interesting to play with.

I thought that jumbling was when 2 mechanically different pieces are able to switch positions and the puzzle can still function...

That's what I was told as well (never got how it was possible though)

Here is a crude sketch of what is going on inside the Helicopter Cube during jumble moves.

viewtopic.php?p=48801#p48801

As for how it's possible, it's simply a consequence of the mechanics of twisty puzzles. Sometimes you can do a twist that aligns those strange circles. If your mechanism was designed in a normal way, then this extra twist will probably be allowed.

Here is my two cents:

Shape Shifting:
changes shape

Jumbling:
where 2 completely different peices (corner/center) can swap places and the puzzle still be able to function properly.

So how do you explain the 24 cube where all 24 pieces are the same?

The precise definition of jumbling has was discussed at length.
Allagem already posted a link to the thread in this topic. It's some really neat stuff.

Another puzzle that supports this theory is the "Pyracopter":

http://www.youtube.com/watch?v=oeOFPOY8 ... annel_page

Its clearly a 3x3 mod, but its also jumbleable in my opinion.

But of course!!!
Look at the math patterns...
Rhombic Tricontahedron Core (jumbling) made from combo of dodecahedron and its dual(icosahedron)
Rhombic Dodecahedron Core (jumbling) made from combo of cube and its dual(octahedron)

Since there are five regular platonic solids and we've only used four so far, it fits the pattern that there should be another:
Combo of tetrahedron and its dual(another tetrahedron) makes a cube

All 3 resulting cores have rhombic faces!!!!!! (remember a square is a rhombus ) and so must all fall in the same pattern as being jumbleable which can clearly be shown by your example. Ofcourse on a Rubik's Cube, restricting movement to only 180 degrees proved very challenging, but possible Does this mean we can make normally jumbling puzzles where the jumbling moves are blocked internally?

Hmmmmm

Peace


PS: Tyler: I was also looking at the Polaris thread. It's looking very nice. The first Icosahedral based puzzle I believe. But is it jumbleable? I see exactly what you mean, the angles do work out and this can be demonstrated by simply looking at an icosahedron. Jumbling occurs when the faces around a given face do not all express radial symmetry. On the rhombic cores this is obvious. On an icosahedron, this does not occur with immediately adjacent faces..... but it DOES with the next set of faces out. Now I am hesitant to make a judgment on this because I am still (like so many others I'm sure) not 100% comfortable with jumbleability by I have a hunch that the non-adjacent faces will give you a problem. From a strictly mathematical sense, it would appear icosahedral puzzles can be considered jumbleable, but I think it is mechanically IMPOSSIBLE. The jumbling moves would interfere with other internal parts. How is this project coming along? Do you have anything working that you can guarantee the puzzle is jumbleable? Again, I'm not sure, but I have a hunch the jumbling won't work.

But it's NOT jumblable. You said it yourself, it's a 3x3 mod. A 3x3 is a 3x3 is a 3x3 no matter the shape it's outside takes.
A jumblable puzzle can change shape, but changing shape does not automatically mean it's jumblable.

Oh, and Allagem. Deeper cut face turning icosahedra are jumblable too.

Lol, did you see the other thing I posted?(it's really small!!!)

I know exactly why you say deeper cut icosahedra puzzles are jumbleable, but I'm suspicious that it won't work mechanically. Do you have a prototype or anything that shows this jumbling in action??

The idea that it's jumbling just BUGS me, and I'm not sure why

But I could be in total denial here....
Maybe I'm wrong and icosahedra are also jumbleable... Wow does that make things interesting. That means roughly 20 more of gelatinbrain's puzzles are jumbleable than I originally thought. Interesting stuff....

Peace

Wow, that's a LOT of text in that little line.
In all truth, I think that the non-adjascent sides would make the puzzle easier to jumble. That's a whole bunch of parts in the internal mech that don't have to interact with each other. If this was the deep cut icosahedron, then the block of pieces that hold the internal mech stable might interfere, but I didn't go that far. However, as I follow the parts around in my head, the jumbling seems very very possible.
I'm heading off to work right now and I'm on LONG (12 hr + Saturday) overtime but if I get a chance, I'll run the twists into a model of the mech rather than just the facade.

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You know, the more I think about it, the more I'm starting to believe that maybe it is possible. Certain internal pieces would be unaffected by the jumbling move, but beyond a certain point, the internals do jumble.... maybe....
I would really appreciate that picture as I'm sure others will. How is the building coming btw? Are your other projects still preventing your work on it? If so how are THOSE coming along?? I wish I had the funds to get some pieces printed because I know EXACTLY how you're designing all of these.... I just have no means of printing my designs

Thanks for coming up with designs that really make me re-think my understanding of puzzles!!!

Peace

well, are all the pieces the same mechanically?

Yes, I believe they are.

They are, but internally there are other pieces that would have to swap places.

I think a better definition has to do with the shape of the core. Here is my definition of jumbleable puzzles:

First off, a puzzle resulting from a certain core shape can rotate around an axis through the center point and perpendicular to a given face. If such a rotation maps the edge between the rotating face and an adjacent face onto a new edge where the angles between the meeting faces are equal, a succesive rotation about the new face is possible
Now then, a puzzle is jumbleable iff the set of all angles that allow such succesive rotations for a given face does not show radial symmetry.

HOW'S THAT!!!!

A few quick notes:
The angles that are not radially symmetrical with 0 degrees are jumbling moves; the angles that are are not
The angle equality I mentioned IS true for every core ever used so far(it would NOT be the same for non-platonic solid cores, such as the one required for an edge-truning rhombic dodecahedron)
If TBTTyler is right, and the icosahedron does show jumbleable qualities, the word 'adjacent' needs to be removed from my definition. In the Polaris's case, the potentially jumbling moves occur at edges outside of the puzzle (that only exist if you extend faces beyond the natural icosahedral shape, one of the reasons I'm unsure of whether or not it will work )

Peace

I like it, though I would figure out some way to remove/change the part about "the center point and perpendicular to a given face" because the viewable faces of a puzzle don't necessarily have anything to do with it's internal structure.

Oh, I guess I wan't clear enough about that. I meant the "face" of the core shape, not the outside shape

Peace

When I first started browsing, I thought jumble and shape changing were the same thing. I now know they're not, even if I don't completely understand why. I think the picture posted with the circles about the helicopter cube is the best example of jumble compared to shape changing.

That is incorrect. For example, if you extend the 2x2x2 to allow 45 degree returns of each face and hence make extra cuts through all the pieces, you then have a jumble puzzle because no amount of unbandaging will ever make it into a simple closed group.

But irrational angles are certainly a sufficient, if not necessary, criterion for being a jumble puzzle.

Wouldn't such a puzzle be the combination of the 24 cube and a 2x2x2? Then along the 45deg plane (where I presume the jumbling action happens) the radial symmetry is broken.

This seems consistent with Allagem's defition to me.

Though I agree that to differentiate a jumbled puzzle from a bandaged one, we must include irrational angles in the definition.

A simpler example to explain is battle gears - that puzzle is actually jumbling although it's 'almost' bandaged because it takes a few iterations before the pieces really turn into dust. The amount the pieces on it move are clearly 45 degrees, which obviously isn't an irrational amount, but the interaction between the two wheels makes it a jumble puzzle.