This is a list of puzzles that jumble. I will ubdate the list when a new puzzle is noted in a comment or when I find one in the forum. Please help me with calculating angles.

The list below is broken up into subgroups based on the angle of rotation needed to preform jumbling moves.

Rational Jumbling
2x2x2 plus partial Helicopter Cube:90 degrees
Split Hex:30 degrees
Mixup 2x4x4:30 degrees
Square1xp:90 degrees
Distorted Cube:92 degrees
Uncanny Cube:45 degrees
Canny Uncube:45 degrees
Shallow Mixup Cube:45 degrees
Bermuda Cubes:45 degrees

Irrational Jumbling
Rua
Face-Turning Rhombic Dodecahedron:≈70.53 degrees
Toru:≈70.53 degrees
Helicopter Dodecahedron
Starminx 2
Big Boulder
Master Helicopter Cube:≈70.53 degrees
Curvy Copter 1 & 2:≈70.53 degrees
Rua tekau ma-wha/24 Cube/Little Chop:≈70.53 degrees
Helicopter Cube:≈70.53 degrees
Combo Copter:≈70.53 degrees
E. T. H. A. N. (master 24 cube):≈70.53 degrees
Lotus II:≈78.04 degrees
Astroid Attack:≈78.04 degrees
Quad X:≈70.53 degrees
Starminx III
Novaminx
Master Skewbminx
Spiral Fracture
Face Turning Tetragonal Trapezohedron
Alphaminx
Jumble Prism
Fracture-6
Fracture-10
Jumble Trap
Jumble Trap Unbandaged
Jumball
Compound Fracture
Twisted-8
Twisted-6
Rhombic18
FTRD:≈70.53 degrees
Pregnant Prism:Irrational Jumbling?
More Madness
Crazy Comet
Meteor Madness

Rational and Irrational Jumbling
Cross Cube/48 Cube:45 degrees, 90 degrees, and ≈70.53 degrees
Helicopter Skewb:60 degrees and ≈70.53 degrees
Fairly Twisted:120 degrees and ...
Fairly Fudged:120 degrees and ...

Undefined
Pascal's Jumble 1 & 2:Rational Jumbling?

distorted cube.
Pascal's Jumble 1&2

Curvy Copter I and II (TomZ)
Master Helicopter Cube (pirsquared/Eitan)
Big Boulder (Oskar)
The Heptagon (Oskar)

Where can I find a clear and precise definition of "jumbling" versus "shape shifting"?

Starminx II

According to Bram (probably the greatest expert in this area): "a jumbling twisty puzzle cannot be unbandaged into a doctrinaire twisty puzzle".

There's already a whole topic and detailed discussion on jumbling puzzles here.

The Heptagon does not jumble. (Oskar made a post correcting himself in the original thread)

Thanks for the help so far. I didn't know half of these even existed.

Helicopter Dodecahedron.

Pregnant Prism from Bram and Oskar

Wouldn't Oskar's Mixup Cube and 2x2x4 Mixup also fall into this category?

No, they do not jumble. They just change shape.

Thanks, but this thread just talks about jumbling puzzles and everybody understands what it means, Some people on this planet understand the difference between "shapeshifting" and "jumbling", some not. I'm still in the second category - and I bet, quite a few others with me. Following Bram's definition, the only two things I need a definition for are "doctrinaire twisty puzzle" and what "unbandaging" means in any specific case.
I really like the idea, that I go to a patent office and want to get a patent for a jumbling puzzle. As a precise and clear definition of the term "jumbling", I'll present the two diagrams I've got as a first answer.

Jumbling has absolutely nothing to do with changing shape - they are two very different concepts. Luck would have it many jumbling puzzles change shape, but it's perfectly possible to have a jumbling puzzle that doesn't change shape (like the helicopter sphere).

For my attempt at explaining what jumbling is, I will use the HC sphere as an example. Here I have turned the yellow centre by 70.3some degrees, the angle at which the HC jumbles:

The purple centre can now make turns but the red centre is blocked.

The red centre can be unblocked by cutting the blue pieces and the yellow centre. In a sense it is a bandaged puzzle.
Cutting a blue piece gives you a piece that is identical to a helicopter cube corner and one other piece. This other piece however, again behaves bandaged on some turns. You could cut this piece in half to enable more moves. This again results in pieces that behave bandaged.

It turns out you can actually keep cutting up pieces but will never get a puzzle that does not behave bandaged. A jumbling puzzle will always behave bandaged no matter how often you slice it up, whereas a bandaged puzzle can be sliced up into a normal "doctrinaire" puzzle.

Is there any shapeshifting (not jumbling) puzzle where moves are blocked in this way??

Uh... Let's say you took a bandaged cube and "fishered" it. Presto!

But really... leave shapeshifting out of this. Jumbling is far more fundamental as it happens on the mechanism level, rather than the outer appearance level.

Thanks Tom! That has been very nice of you helping out the poor guys - like me - who had a vague understanding of jumbling only. With this explanation by example the definition of Bram makes perfect sense.

My clearest definition is: the puzzle jumbles if when a certain move is completed, it blocks the movement of another turn

So would you think the Square 1 jumbles?

With most jumbling puzzles, mechaniclly they become a different internal puzzle after being jumbled. Because of this, a 2x2x2 and skewb for example could be within a jumbling puzzle. After a few random rotations on this hypothetical puzzle, paths could become blocked and only 2x2x2 rotations could work. This puzzle could then be jumbled again and it would be possible for only skewb rotations to be made. In most jumbled states however, it would be a mix between a 2x2x2 and a skewb.

Thanks TomZ for that explanation, I get jumbling now.

Alex

The SQ-1 is actually hard to define if it does or doesn't. Sure, you can cut the corners and make it a SQ-2, and that'd be removing the "bandaging" that's on it. But then you can cut it more. And now it has "bandages" again.

You can cut it infinitely, while still maintaining working cuts, and bandaged cuts.

A Square 2 is not bandaged so I don't get what your saying. Why would you cut it again? If enough people agree with you I'll ad it to the list.

Why not? I mean, you CAN cut it again, without messing up the mechanism or the workings of the puzzle. If you cut all the original edge pieces in half, you'd have another puzzle, with some moves blocked, and you can repeat this forever.

I wouldn't call it jumbled, but I wouldn't say it's just shapeshifting either. IDK, the SQ-1 is weird for a lot of reasons.

If a square 1 was built with a different internal mech, it's still a Square 1. A 3x3x3 might exist that can be cut over and over without messing up the mechanism, but that doesn't make a 3x3x3 jumble.

I agree that the Square 1 is special but becuase it changes shape, it's a shapesifter in my opinion.

Argh... how often do I need to say this: Jumbling is completely unrelated from shapeshifting!

A square one doesn't jumble. There are infinitely many possibilities for cutting up the pieces but only so many for unbandaging them.

This gave me an idea, bandage a Square 1 into a non bandaged puzzle.

Also I am adding links to the list. If links are known, they would be helpfull.

Hi Jumble Enthusiasts,

Bram and I wrote a full-length article about Twisty Puzzle that Jumble, which I have submitted to Sandy. Unfortunately, I am on Sandy's spam filter, and from the lack of response I suspect that none of my messages have arrived. I hope that this article can be published at Twisty Puzzles Articles some time.

Oskar

Great article When was jumbling first recognized? I independently discovered jumbling a while ago and it would be cool if I was one of the first to get frustrated by trying to "unbandage" a jumbling puzzle.

Great article, I need to get myself a subscription to CFF...
I think jumbling is a very fascinating occurence, although I don´t really like the blocking capabilities too much. For instance I would much rather get the Meteor Madness instead of More Madness.

So there is only one commercially available jumbling puzzle at the moment, the Helicopter Cube?

Would the Siam Mandalay's Setting Sun puzzle be considered a puzzle that jumbles?

I made the following argument why Mixup Cube jumbles: "If you turn one face by 45 degrees, then you can do some unbandaging, and continue unbandaging". Bram argued why Mixup Cube is (just) a shape mod of a doctrinaire puzzle: "After any regular turn (90 degrees for the sides, 45 degrees for the slices), the puzzle is restored to its original state (except for shape and sticker changes)".

With Bram being the expert on jumbling, the verdict would be that that the Mixup puzzles do not jumble.

Oskar

My thoughts on the square-1:

Pucks make up a 2-dimensional infinite series of doctrinaire puzzles.
The two dimensions for a puck are number of layers and number of slices.

Square-1 is a 3-layer, 12-slice puck with the following alterations:
1. The top and bottom layers alternate between an unbandaged slice and two slices bandaged together.
2. The middle layer is bandaged into 2 equal pieces.
3. The puzzle is shape-modified into a cube.

Square-2 is also a 3-layer, 12-slice puck but only with alterations 2 and 3. Super Square-1 and Four-Layer Star Prism are both bandaged shape mods of a 4-layer, 12-slice puck while the 4-Layer Dodecahedral Prism is their doctrinaire counterpart.

When you cut a Square-1 edge in half, you enter the territory of bandaged, shape-modified 24-slice pucks.

Thank you very much! I fell much less stupid recognizing that even the experts are debating if a puzzle jumbles or not
Tom's explanation above and this article make the definition clear and precise.

The point has been made by Oskar in the meantime but I still want to answer this:
It is possible to (technically) bandage a 4x4x4 into a 2x2x2 which is not a bandaged puzzle. Bandaging (in this context) doesn't mean a technique of modding but a class of puzzles.

I think that Square-2 is a "restricted" puzzle. The 3x3x3 is not.
On a 3x3x3 there is always one move by which one could "cut" between every of the 54 gaps (6 are invisible) the 3x3x3. On the Square-2 not every gap between two pieces can be used for a move. An "unrestricted" Square-2 would be the 3-layer 12-slices puck with just alteration 3 Jeffrey mentioned.
Another way to distinguish between "restricted" and "bandaged" would be this:
On a bandaged puzzle the sides which allow turning depend on the permutation of the puzzle. On a restricted puzzle it depends only of the puzzle itself. This means the FusedCube is not bandaged but "just" restricted.

I came up with this difference after I tried to "unrestrict" the SeniorBarrel, which is restricted but not jumbling.

I agree but if the 2x2x2 did not exist, a 4x4x4 could be bandaged into that new puzzle. Kind of like 2x2x6 cubes that are just 6x6x6s bandaged.

On topic, what puzzles are still missing from the list?

Eitan's Face-Turning Rhombic Dodecahedron

Here's a video of the Rua

With all this talk about if the square 1 jumbles, I am adding the Square1xp to the list. If you don't agree with me that it jumbles please say so.

I would not consider a Square-1 to jumble because mechanically, the mechanism always stays the same, unlike a helicopter cube or some other jumbling puzzle.

P.S. - No, I'm not a new member, I just had a username change. (I used to be Cheese_Board)

No, neither the square one nor the square1xp jumble.

Then design a nonbandeged square1xp. You would cut the puzzle to dust. That is why I believe it jumbles. Mechanically a square 1 stays the same. The square1xp mechanically does change because the internal 2x2x2 when scrambled, relocates the square 1 mechanism.

The Square1 does not jumble, because it can be unbandaged to a Square2, which can be shape modded to be cylindrical, so it's just a bandaged and shape modded puzzle.

The Square1xp most definitely does jumble though. You can unbandage it somewhat to be a Square2xp, but if you start trying to add in slices in all three direction to every corner it will very rapidly turn to dust. The comparison to its close cousin the 2x2x4 is interesting, because they have slices in the same places but rotate a different amount on some of the same slices, which makes them quite different.

With regards to mixup puzzles, the regular Mixup Cube does not jumble. If you mod the shape to a sphere, there are two moves, one to rotate a face 90 degrees, and another to rotate a center slice 45 degrees, and both leave the puzzle exactly the same. The Mixup 2x2x4 does jumble though. At least I think it does, I'm still having some trouble wrapping my brain around that one. If anyone has an idea how to unbandage it I'd like to see.

What would a sphere version of the mix up 2x4x4 look like?

It would look like a sphere, I think...

-Ï€ (Eitan)

I was meaning the lines but that is also correct I guess. I think I figured it out and I believe it could be made so that it doesn't jumble. Each edge piece would need to be cut into four pieces.
http://twistypuzzles.com/shop/index.php?main_page=product_info&products_id=114

The puzzle in the link is kind of like what I mean.

Answering my own silly question, the mixup 2x4x4 is based on the split hex, which clarifies both how it works and that it does, indeed, jumble -

http://www.shapeways.com/model/102161/split_hex.html

The split hex should be added to the list of jumbling puzzles, as should battle gear -

http://www.jaapsch.net/puzzles/battlegear.htm

So is the mixup 2x4x4 a bandaged version of the split hex? Also I still believe it would be possible to make a mixup 2x4x4 that doesn't jumble.

(I might as well mention that the Hex Cube, which is a bandaged Split Hex, could possibly be extended into a Mixup Domino. But does the Hex Cube jumble or not?)