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 Post subject: Re: Puzzles that jumble
PostPosted: Sun Jun 27, 2010 9:52 pm 
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Yes the mixup 2x4x4 is a bandaged split hex.

No the mixup domino would not jumble, for the same reason the mixup cube doesn't jumble.


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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 1:55 am 
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But then what makes the Split Hex jumble, if it's an "unbandaged" Mixup Domino? :|


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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 2:29 am 
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Jared wrote:
But then what makes the Split Hex jumble, if it's an "unbandaged" Mixup Domino? :|

I believe it's an unbandaged mixup 2x4x4, not mixup domino. If the Split Hex was bandaged into a 2x3x3, the moves that allow it to jumble are covered up. It's kind of like a 5x5x5 being bandaged into a 3x3x3. The pieces that make it a 5x5x5 do not mechanically exist just like the pieces in the split hex that allow it to jumble would mechanically not exist if it was bandaged into a Domino.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 5:47 am 
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One thing that I just thought about - Does my 2x2x2 + partial helicopter cube jumble? When scrambling like a 2x2x2, the helicopter cube-type cuts get blocked. Trying to unbandage it results in a 2x2x2 + helicopter cube, which definately does jumble. Any ideas?

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 9:44 am 
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I think a 2x2x2 + partial helicopter cube does jumble. Like you said, that will unbandage to a 2x2x2 + helicopter cube. And by the definition of a jumbling puzzle,

Jumbling Puzzle + More Cuts = Jumbling Puzzle

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 11:52 am 
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I agree that your puzzle jumbles but to advertise it as jumbling would be slightly misleading. A buyer would expect it to jumble like a helicopter cube, which it can't.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 1:23 pm 
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I never advertised it as jumbling. :? (Do you see the word "jumble" anywhere on my Shapeways page?) I only pointed out that it can technically be added to your list of jumbling puzzles.

Also, are there any other puzzles that jumble like my puzzle does? (I'm trying to think of a way to describe this type of jumbling, but I'm not quite sure how)

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 1:37 pm 
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will_57 wrote:
I never advertised it as jumbling. :? (Do you see the word "jumble" anywhere on my Shapeways page?) I only pointed out that it can technically be added to your list of jumbling puzzles.

Also, are there any other puzzles that jumble like my puzzle does? (I'm trying to think of a way to describe this type of jumbling, but I'm not quite sure how)

I think you should advertise it as jumbling, just include that it is different then a Helicopter cube's jumbling.

Also I agree that jumbling might have subgroups. Your puzzle could fit in the group "jumbling puzzle bandaged into non jumbling state with an infused non jumbling puzzle allowing the resulting puzzle to jumble" group. The square1xp would kind of fit in this catagory, along with a few puzzles I am working on :D
This brings up an even harder question then what makes a puzzle jumble, what subgroups exist within jumbling puzzles?

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 2:09 pm 
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Does Mixup Cube jumble or not?

There are two ways of looking at this. Its basic rhombicuboctahedron geometry looks pretty doctrinaire (first drawing). However, when projecting this on its Jaap's Sphere, there are two design options.

Option 1: Fudged
The basic projecting as shown in the second drawing. Each turn will result in a little click.

Option 2: Jumbled
This projection has smooth turning. There are little crevices between pieces, see third drawing.

In my design for Mixup Cube, I choose the latter approach, using some shape modding to hide the crevices.

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Attachment:
Mixup Cube - rhombicuboctahedron.jpg
Mixup Cube - rhombicuboctahedron.jpg [ 31.42 KiB | Viewed 4928 times ]

Attachment:
Mixup Cube - fudged.jpg
Mixup Cube - fudged.jpg [ 51.85 KiB | Viewed 4928 times ]

Attachment:
Mixup Cube - jumbled.jpg
Mixup Cube - jumbled.jpg [ 51.72 KiB | Viewed 4928 times ]

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 2:30 pm 
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Here are my thoughts on different kinds of jumbling
Jumbling combination puzzles that can only jumble if certain kinds of pieces are in certain orientations and permutations (like the square1xp, if it is actually a jumbling puzzle), could be called "opportunity jumbling".

Jumbling on puzzles like the helicopter cubeand Oskar's Crazy Comet is different. The faces can turn 180 degrees in order to end up with a doctrinaire twistypuzzle, or turns of 70.5 (?) degrees where the puzzle does in fact jumble. So the jumbling can be done with every turn, but it's optional. So this could be called "optional jumbling".

And finally there are puzzles in which every move is a jumbling move, such as the Meteor- and More Madness, the Astroid Attack and the Big Boulder.
This could be called "forced jumbling" or "inevitable jumbling".

The "optional jumbling" puzzles I mentioned are both based on rhombic dodecahedra, and I think every rhombic dodecahedron based puzzle (that jumbles (but I believe all of them do)) have "optional jumbling".
Puzzles based on a rhombic triacontahedron, like edge-turning dodecahedra, also have this "optional jumbling".
Rhombusses have rotational symmetry by 180 degrees (I know this has a different name, but I can't seem to find the english word for it).
So in conclusion about "optional jumbling", (most) twistypuzzles based on shapes with faces that have rotational symmetry by 180 degrees have "optional jumbling".

However, the turning faces on the puzzles with "inevitable jumbling" do not have faces with rotational symmetry by 180 degrees, but reflection symmetry. And maybe even irregular symmetry, but I can't think of one that exists right now.
For example, the Astroid Attack puzzle is based on the tetragonal trapezohedron, which has kit'-shaped faces.

I can't think of any other kind of jumbling than the ones named here.
I propose these names, or at least these categories, for the classification of jumbling puzzles.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 3:04 pm 
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Oskar's first picture shows why I think the mixup cube doesn't jumble. Rotating an inner slice by 45 degrees leaves the puzzle exactly the same.

Maybe another kind of jumbling puzzles could be if one or two systems allow the puzzle to jumble. The helicopter cube I would consider one system because it only has one way to twist it. The 2x2x2 plus partial helicopter cube would have two systems because the 2x2x2 and helicopter cuts don't intermix.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 3:07 pm 
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PuzzleMaster6262 wrote:
Oskar's first picture shows why I think the mixup cube doesn't jumble. Rotating an inner slice by 45 degrees leaves the puzzle exactly the same.

I dont see how if you turn it 45 degrees it stays the same it looks like to me there will be moves that are blocked


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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 3:35 pm 
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eye2eye wrote:
PuzzleMaster6262 wrote:
Oskar's first picture shows why I think the mixup cube doesn't jumble. Rotating an inner slice by 45 degrees leaves the puzzle exactly the same.

I dont see how if you turn it 45 degrees it stays the same it looks like to me there will be moves that are blocked

The triangle pieces stay in the same place. When a band of squares rotate, every 45 degrees they would not block any rotations.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 3:57 pm 
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ok i see it now i was looking at the wrong picture im sorry.


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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 4:06 pm 
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Sjoerd wrote:
Here are my thoughts on different kinds of jumbling
Jumbling combination puzzles that can only jumble if certain kinds of pieces are in certain orientations and permutations (like the square1xp, if it is actually a jumbling puzzle), could be called "opportunity jumbling".


If you made a 24-cube which only allowed 180 degree turns, then it would be a non-jumbling puzzle. This is, ahem, surprisingly difficult to design. You could also restrict Battle Gears to 90 degree turns instead of 45, and that wouldn't jumble either.

The quasi-mathematical term for what you're talking about is having a nontrivial finite subgroup.


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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 4:09 pm 
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Oskar wrote:
Does Mixup Cube jumble or not?

There are two ways of looking at this. Its basic rhombicuboctahedron geometry looks pretty doctrinaire (first drawing). However, when projecting this on its Jaap's Sphere, there are two design options.


There's a third option - add in a bunch of tiny pieces to fill in the gaps. There wouldn't be much of any practical benefit to that - they'd be very small and non-functional, but it would work. Just because a puzzle looks funny in Jaap's applet doesn't mean it doesn't work. For example, the Starminx II is very hard to visualize using that tool, because of the way the layers interact, but it does in fact work just fine.


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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 7:33 pm 
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Bram wrote:
Sjoerd wrote:
Here are my thoughts on different kinds of jumbling
Jumbling combination puzzles that can only jumble if certain kinds of pieces are in certain orientations and permutations (like the square1xp, if it is actually a jumbling puzzle), could be called "opportunity jumbling".


If you made a 24-cube which only allowed 180 degree turns, then it would be a non-jumbling puzzle. This is, ahem, surprisingly difficult to design. You could also restrict Battle Gears to 90 degree turns instead of 45, and that wouldn't jumble either.

The quasi-mathematical term for what you're talking about is having a nontrivial finite subgroup.


The piece of text you quoted is about opportunity jumbling, but the 24-cube would be in the category of optional jumbling, since it is based on the symmetry of a rhombic dodecahedron (I explained this in my previous post).
If what you say about the Battle Gears is correct, it would also have optional jumbling, but would not fit in with my conclusion since those statements were based on threedimensional shapes.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 10:00 pm 
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Dear Lord this topic has gone in several directions at once, and many of them with some awkward and misled conclusions... :?

I used to post quite frequently but do only rarely now. However, I have been keeping track of the posts. Although I wouldn't compare myself to the genius of Bram and Oskar who have made these wonderful inventions, I have been studying all of Oskar's twisty creations and consider myself something of an expert. However I don't wish to come off as rude so let me just add my thoughts to this conglomeration of assertions and you can decide for yourself if they make sense :)


1. Is the Square-1 a bandaged puzzle or a jumbling puzzle?

BANDAGED. As someone pointed out, this means you should be able to unbandage it, and indeed you can!!! The Square-1 is based on the geometry of a dodecahedral prism. I am currently on a laptop in a hotel in Maine and do not have a CAD software with which I can draw it, but the unbandaged Square-1 has ALL three layers cut into twelfths. This means there are 6 vertical cuts, all of which are Deep-cut. The actual Square-1 puzzle only has one of these vertical cuts and therefore can use a shortcut-mech, eliminating the need for a core and instead screwing the two middle layer pieces directly together. Including all 6 vertical slices requires a much more complicated, but still possible mechanism.


2. What about the Mixup Cube, Hex Cube, Split Hex, and Mixup 2x4x4?

I have hinted in some of my posts that I have a very rigorous requirements for what is and what is not a twisty puzzle. I do this for a reason. Anything that passes falls very nicely into every category that we discuss here: jumbling, bandaged, shapeshift, deep-cut, etc. One of these requirements is that a twisty puzzle has a geometrically stable core, possibly infinitessimal. The Mixup Cube, Hex/Split-Hex Cube, and Mixup 2x4x4 Cube all FAIL this requirement. Here's why:

Let's assume there is a stable core in the mixup cube: start with the puzzle aligned with the xyz axes. We know we can turn both the top and bottom layers 45 degrees and then swap two centers around the middle. This implies that there is a rotation point, a plane of rotation just like all other twisty puzzles have, around a ray that juts out of the core at every 45 degrees along the xy plane. In fact we can apply this again to find rotation points at 45 degrees around the xz and yz planes as well, leaving us with a grand total of 18 rays emerging from the core around which the puzzle can be rotated at some point, right?

Wrong. There are even more 8-) That rotation that swaps two centers can be stopped at multiples of 90 degrees, even 45 degrees provided the opposite face is also rotated an odd multiple of 45 degrees. This opens up more rotations that spin around previously unmarked rotation points. This means there must be at least 8 additional rotation points per rotation point that we already have, each of which have an additional 8 branching from it and so on till infinity. You get a very similar problem to how jumbling puzzles were discovered in the first place. Instead this one requires an infinite number of rotation points (rays extending from the center) that cut the puzzle into infinitesimal points bandaged into the pieces you see. Ipso Facto: these puzzles are not twisty puzzles. :wink:

There are a few other puzzles that behave this way, namely the Massage Ball, The Chromoball, and a few others. Would you consider these puzzles to be standard twisty puzzles? I wouldn’t. And in actuality, the Mixup Cube is a combination of a 2x2x2 and a modified Chromoball. The Hex Cube family is an even more creative application of the same idea. And again, these puzzles do not have stable cores.


So are they bandaged or jumbleable? I say neither. They are bandaged in the same sense that a 3x3x3 is a bandaged 6x6x6. Does that count? I don’t think so. And I personally define jumbleability by the core shape, and these puzzles have no core shape, save for the 2x2x2 pieces, which of course function exactly like a normal 2x2x2 which is neither bandaged nor jumbleable. It is exactly the same as classifying the Chromoball. I don't think bandaged and/or jumbling really apply.

I can try to draw the unbandaged Square-1 in the next few days as soon as I get back home from vacation. Of course if someone else is following me, they're certainly welcome to draw it too :D

Oskar's puzzles continually redefine what we know about Twisty puzzles and we have to continually edit our understanding of them. I personally believe I have developed a system that explains all of the puzzles simultaneously and that has not come easy. I have come up with these conclusions through observations, making and testing hypotheses, and having an open-mind. I hope my explanations make sense :) and please feel free to argue if you disagree :lol:

And Oskar/Bram (I'm starting to get confused as to who does what exactly), as long as you make these beautiful and clearly mind-boggling creations, I will try my best to understand EXACTLY how they work :wink:

Peace,
Matt Galla
PS: Really? A Square-1 is a jumbling puzzle? Sheesh, a new concept is discovered and everyone starts calling wolf on everything lol. A Square-1 always has been and always will be a cubical shape mod of a bandaged three layered, deep cut dodecahedral prism puzzle based twisty-puzzle. What part of that doesn't make sense ; )

Edit: 2 things regarding the Square-1 area:

1. I just realized we are talking about multiple square-1's here. My explanation above applies to the standard square-1 (and square-2). I need to study traiphum's square-1xp much more closely. It's a tricky little bugger. I'm not sure about that one's jumble status yet.... :roll:

2. Back on page one, Jeffery Mewtamer got it exactly right. I apologize for not giving him credit above, I missed it the first time. :wink:


Last edited by Allagem on Mon Jun 28, 2010 10:44 pm, edited 1 time in total.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 10:35 pm 
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I agree about the square 1 being bandaged. As for the mixup cube, it only has 18 pieces that can act as centers so I don't understand why you think it has infinite.
(the square1xp does jumble. I'm making a square 1 that does jumble)

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 10:49 pm 
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True, except that on standard twisty puzzles, centers don't move around :wink:
Try to design a core that doesn't move for this puzzle (that is the center pieces that connect directly to the core don't move either, they merely rotate in place just like a normal Rubik's Cube's centers.)
Attempting to design such a core results in the "dust" scenario for a much different reason than jumbling.

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 Post subject: Re: Puzzles that jumble
PostPosted: Mon Jun 28, 2010 11:00 pm 
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But jumbling shouldn't invlove what is on the inside of a puzzle. On a side note, the knuckle head concept could be used along with hidden pieces to make a mixup cube without "fudging".

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jun 29, 2010 8:05 am 
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PuzzleMaster6262 wrote:
But jumbling shouldn't invlove what is on the inside of a puzzle. On a side note, the knuckle head concept could be used along with hidden pieces to make a mixup cube without "fudging".

Jumbling should only involve what's on the inside of the puzzle.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jun 29, 2010 8:20 am 
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All vertex-turning pentagonal dodecahedra where 2 non-adjacent corners on each face-pentagon overlap can also jumble. I used Jaap's sphere applet, and it appeared to work for all vertex-turning dodecahedra...can anyone please explain exactly WHY this is? (it does explain why the Polaris would jumble though....) sorry for the very improper usage of grammar and math, but that's about as far mathematically as my brain can go with this ._.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jun 29, 2010 9:12 am 
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theVDude wrote:
PuzzleMaster6262 wrote:
But jumbling shouldn't invlove what is on the inside of a puzzle. On a side note, the knuckle head concept could be used along with hidden pieces to make a mixup cube without "fudging".

Jumbling should only involve what's on the inside of the puzzle.

Jumbling only involves how the pieces move. What I was saying was the internal mechanics that allow the puzzle to exist have nothing to do with jumbling. A 3x3x3 is just a 3x3x3 even if it has hundreds of internal pieces allowing it to work.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jun 29, 2010 9:30 am 
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Misunderstood you. I thought you were talking about the appearance of the puzzle.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jun 29, 2010 10:06 am 
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The three different types of sphere on gelatinbrain jumble as well. Or was the list restricted to built puzzles?

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jun 29, 2010 10:10 am 
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I'm restricting the list to built puzzles only. An exception might be if the puzzle is fully designed and currently being built.

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 Post subject: Re: Puzzles that jumble
PostPosted: Tue Jun 29, 2010 10:27 pm 
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I think I have figured out the best way to quickly and simply create subgroups for jumbling puzzles. If my idea gets positive feedback, I will include my subgroups in my list of jumbling puzzles. The groups are based off "rational jumbling" and "irratinial jumbling". An example of rational jumbling would be the 2x2x2 plus partial helicopter cube. To preform jumbling moves, the 2x2x2 is rotated by 90 degrees, a rational number. A full helicopter cube however would have irrational jumbling because to preform jumbling moves, an edge is rotated about 70.1 degrees, an irrational number.

Jumbling puzzles with only rational jumbling would go in the rational subgroup.

Jumbling puzzles with only irrational jumbling would go in the irrational subgroup.

Jumbling puzzles with both rational and irrational jumbling would go in the rational and irrational subgroup.

Then each subgroup if needed could be expanded with subsubgroups if members feel this is to wide of a range for each subgroup.
The reason I like this idea over other options is all puzzles can quickly be subgrouped. There is no need for gray. Also I feel these subgroups split jumbling evenly.

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 Post subject: Re: Puzzles that jumble
PostPosted: Wed Jun 30, 2010 11:02 am 
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70.1 isn't irrational, but I hope you don't think so too. Anyone know what the actual number is? Just curious.

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 Post subject: Re: Puzzles that jumble
PostPosted: Wed Jun 30, 2010 11:27 am 
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the exact measure cos^-1(1/3) is for jumbling on the curvy copter, i'd imagine it be the same curvy or not


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 Post subject: Re: Puzzles that jumble
PostPosted: Wed Jun 30, 2010 11:31 am 
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GuiltyBystander wrote:
70.1 isn't irrational, but I hope you don't think so too. Anyone know what the actual number is? Just curious.

PuzzleMaster6262 wrote:
about 70.1 degrees

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 Post subject: Re: Puzzles that jumble
PostPosted: Wed Jun 30, 2010 11:52 am 
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Setting that little tangent aside, what are your opinions about rational, irrational, and both subgroups?

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 Post subject: Re: Puzzles that jumble
PostPosted: Wed Jun 30, 2010 5:48 pm 
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I love these discussions. I wish I had more time to take part in them. Since being employed again my free time is near zero.

Allagem wrote:
2. What about the Mixup Cube, Hex Cube, Split Hex, and Mixup 2x4x4?

I have hinted in some of my posts that I have a very rigorous requirements for what is and what is not a twisty puzzle. I do this for a reason. Anything that passes falls very nicely into every category that we discuss here: jumbling, bandaged, shapeshift, deep-cut, etc. One of these requirements is that a twisty puzzle has a geometrically stable core, possibly infinitessimal. The Mixup Cube, Hex/Split-Hex Cube, and Mixup 2x4x4 Cube all FAIL this requirement.


So... you tell us what they aren't. But in your "developed system" what are they?

Its clear your definition of a twisty puzzle and Oskar's and Bram's definition of doctrinaire puzzle aren't the same. If you pull the two together I could see there being doctrinaire twisty puzzles and doctrinaire non-twisty puzzles. Though I don't think "non-twisty" is the best word choice for this other group of puzzles. Jumbling then would refer to the non-doctrinaire twisty puzzles. Is there a group of non-doctrinaire non-twisty puzzles? If I understand the definitions used the answer would be yes, I think.

Examples:
doctrinaire twisty puzzle: 3x3x3
doctrinaire non-twisty puzzle: Mixup Cube
non-doctrinaire twisty puzzle: Helicopter Cube (Jumbles)
non-doctrinaire non-twisty puzzle: Hex/Split-Hex Cube and Mixup 2x4x4 (If we don't call these jumbling moves what DO we call them?)

Allagem wrote:
Oskar's puzzles continually redefine what we know about Twisty puzzles and we have to continually edit our understanding of them.


Ahhh... you are now not sticking to your own definition of twisty puzzle. :) As many of Oskar's and Bram's creations fall outside your definition.

Allagem wrote:
I personally believe I have developed a system that explains all of the puzzles simultaneously and that has not come easy. I have come up with these conclusions through observations, making and testing hypotheses, and having an open-mind.


Sounds like the topic of a great paper... or at least a tread of its own. If either exists please point me to it. I eat this stuff up.

Thanks,
Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 1:46 am 
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Battle Gear only has rational angles but jumbles.

In my book, any puzzle which is primarily permutation based is a twisty puzzle, including every puzzle mentioned in this thread


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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 9:24 am 
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Bram wrote:
In my book, any puzzle which is primarily permutation based is a twisty puzzle, including every puzzle mentioned in this thread


I tend to agree and I did say that I thought non-twisty puzzles wasn't the the best name choice for this group/sub-group. But I do see the point Matt is making. You've taken the twisty puzzle group and divided it into doctrinaire and non-doctrinaire twisty puzzles. Using Matt's agrements I could see his definition being used to create two different sub-groups as well. The intersection of these two sets of sub-groups can then be used to classify all twisty puzzles into 4 groups.

Going back to Matt's terminology maybe we could call his two sets twisty puzzles with stable cores and twisty puzzles without stable cores.

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 11:39 am 
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wwwmwww wrote:
Bram wrote:
In my book, any puzzle which is primarily permutation based is a twisty puzzle, including every puzzle mentioned in this thread


I tend to agree and I did say that I thought non-twisty puzzles wasn't the the best name choice for this group/sub-group. But I do see the point Matt is making. You've taken the twisty puzzle group and divided it into doctrinaire and non-doctrinaire twisty puzzles. Using Matt's agrements I could see his definition being used to create two different sub-groups as well. The intersection of these two sets of sub-groups can then be used to classify all twisty puzzles into 4 groups.

Going back to Matt's terminology maybe we could call his two sets twisty puzzles with stable cores and twisty puzzles without stable cores.

Carl

I agree to disagree. The internal mechanics of any puzzle should not be involved when deciding how to classify it. The core of a puzzle is not important. Only the visible pieces involved in solving a puzzle matter. If the mixup cube was created with hundreds of parts and a stable core, it is still a mixup cube.

Also the puzzle list has been moved into subgroups based on rational/irrational jumbling. If possible I would like to include the angle of rotation for each puzzle that allows jumbling moves. If you know the angle, please post it :D

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 2:44 pm 
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PuzzleMaster6262 wrote:
I agree to disagree. The internal mechanics of any puzzle should not be involved when deciding how to classify it. The core of a puzzle is not important. Only the visible pieces involved in solving a puzzle matter. If the mixup cube was created with hundreds of parts and a stable core, it is still a mixup cube.


Matt isn't talking about the physical mechanism of the puzzle. He's looking at the implied core of the puzzle if it were a "pure" twisty puzzle. It does have a physical property that seperates it from "pure" twisty puzzles which is contained in the visible pieces regardless of how the particular internal mechanism works. Think of it this way...

All doctrinaire "pure" twisty puzzles can be thought of as a solid with cut plans that go all the way through the solid and allow rotation.

With that in mind I agree the Mixup Cube is a doctrinaire twisty puzzle but its impure. There are extra cut planes which don't make it to the surface. If you extend those planes to make it pure (similiar to unbandaging) you run into problems which are very similiar to trying to unbandage a puzzle which jumbles.

PuzzleMaster6262 wrote:
Also the puzzle list has been moved into subgroups based on rational/irrational jumbling. If possible I would like to include the angle of rotation for each puzzle that allows jumbling moves. If you know the angle, please post it :D


Personally I see Matt's issue as much more fundamental then the issue of rather the jumbling angle is rational or irrational. Sure both kinds exist but I really don't see the need to treat the two as different subgroups.

The next subgrouping I'd likely make would be 2D vs 3D. I agree with Bram and I'd call the 2D puzzles twisty puzzles too.

Hmmm... I wonder if 4D puzzles can jumble? My brain gets fried just thinking about the most basic 4D twisty puzzles.

http://www.superliminal.com/cube/cube.htm

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 3:19 pm 
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Let's look at the 2D puzzles for a second:

Battle Gear is a twisty puzzle... correct?

What about the 15 puzzle? Should we call that a slidey puzzle? Bram, do you still call this a twisty puzzle?

When I look at a 3x3x3 I see a 3D twisty puzzle. To me the Mixup Cube is an impure twisty puzzle because it has slidey elements to it. It physically is impossible to construct as a pure twisty puzzle. 2D slidey puzzles need a void for the pieces to be able to move but that isn't the case in 3D as loops can be made. Look at the Chromoball for example.

Actually, there are 2D slidey puzzles without voids too. Look at the series of Dave's Elemental puzzles. Again, Bram would you call these twisty puzzles?

So maybe we could call the group I've called "non-twisty" and "impure" above Twisty/Slidey Puzzles. This can also answer the question of what do we call these moves. The rotation of a middle layer of a Mixup Cube by 45 degrees could be called a Slide. And your list of types of moves then becomes:

Twist
Bandaged
Shape-Changing
Jumble
Slide

A puzzle could have some or maybe even all of these types. For example a Helicopter Cube has normal Twists and Jumble moves.

If you assume all puzzles are spheres centered on the crossing point of all axes of rotaion then you can drop Shape-Changing.

Carl

P.S. I still haven't fully understood the Hex Cube, Split Hex, and Mixup 2x4x4. Maybe we have Jumble Twists AND Jumble Slides.

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 3:28 pm 
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I agree with what you are getting at and I like the concepts you noted in your second post.

Rational and irrational are subgroups for just jumbling, not twisty puzzles as a whole.

The mixup cube being a slide puzzle is a good idea but it COULD be made without sliding.

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 3:39 pm 
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PuzzleMaster6262 wrote:
The mixup cube being a slide puzzle is a good idea but it COULD be made without sliding.


How? If I understood Matt's point correctly you'd need to start with a core that had an infinite number of axes of rotation. To me that is akin to saying you can unbandage a jumbleable puzzle with an infinite number of cut planes.

Granted maybe I have misunderstood something, so I really would welcome being proved wrong.

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 3:44 pm 
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wwwmwww wrote:
PuzzleMaster6262 wrote:
The mixup cube being a slide puzzle is a good idea but it COULD be made without sliding.


How? If I understood Matt's point correctly you'd need to start with a core that had an infinite number of axes of rotation. To me that is akin to saying you can unbandage a jumbleable puzzle with an infinite number of cut planes.

Granted maybe I have misunderstood something, so I really would welcome being proved wrong.

Carl

The mixup cube only has 26 pieces (visible), 8 of those are corners so that leaves 18 pieces that can "slide" :D . Each of those pieces can act as a center and only those pieces can act as a center so I believe it can only have 18 axes of rotation.

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 4:40 pm 
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Sorry about the 70.1, I somehow didn't see the "about."

It seems that the general consensus is that the Battle Gear jumbles despite having rational angles. I thought I would try to unbandage it a bit and see where the jumbling occurs. This is what I got.
Attachment:
battlegear.png
battlegear.png [ 11.22 KiB | Viewed 4542 times ]

The standard turn is 45 degrees and as far as I can tell, those are the only turns allowed. Can someone point out the angle of the first jumbling move?

Or am I missing something about your jumbling definition? Do you want pieces to be able to turn on every cut all the time for it to not jumble?

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 4:47 pm 
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GuiltyBystander wrote:
Sorry about the 70.1, I somehow didn't see the "about."

It seems that the general consensus is that the Battle Gear jumbles despite having rational angles. I thought I would try to unbandage it a bit and see where the jumbling occurs. This is what I got.

The standard turn is 45 degrees and as far as I can tell, those are the only turns allowed. Can someone point out the angle of the first jumbling move?

Or am I missing something about your jumbling definition? Do you want pieces to be able to turn on every cut all the time for it to not jumble?

This is how I'm making the subgroups. Because Battle Gear rotates 45 degrees when jumbling, it goes in the rational jumbling subgroup. Check the list on the first page to see the other puzzles that fall in this catagory. Jumbling moves do not need to be irrational, as shown by the first subgroup.

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 5:21 pm 
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But after a 45 degree turn, the other wheel can still turn. Jumbling puzzle have to block turn when they jumble right?

Also, too quote Bram
Bram wrote:
Let's define a 'doctrinaire' puzzle as one where if you were to remove all the coloration then every single position would look exactly the same.

Why isn't this a doctrinaire puzzle? What looks different after a 45 degree turn?

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 5:38 pm 
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GuiltyBystander wrote:
But after a 45 degree turn, the other wheel can still turn. Jumbling puzzle have to block turn when they jumble right?

Also, too quote Bram
Bram wrote:
Let's define a 'doctrinaire' puzzle as one where if you were to remove all the coloration then every single position would look exactly the same.

Why isn't this a doctrinaire puzzle? What looks different after a 45 degree turn?

One of the triangle pieces blocks the other wheel from turning.

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 6:26 pm 
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I still have no idea what you're talking about. You're going to have to spell it out for me. Can you highlight the piece in question in my unbandaging and if possible, show it after the 45 degree turn?

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 6:30 pm 
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PuzzleMaster6262 wrote:
One of the triangle pieces blocks the other wheel from turning.


Not in the unbandaged Battle Gear GuiltyBystander drew above. Since Battle Gear can be unbandaged with a finite number of cuts I would call Battle Gear a bandaged twisty puzzle, not a jumbleable one.

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 7:17 pm 
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PuzzleMaster6262 wrote:
The mixup cube only has 26 pieces (visible), 8 of those are corners so that leaves 18 pieces that can "slide" :D . Each of those pieces can act as a center and only those pieces can act as a center so I believe it can only have 18 axes of rotation.


Ok... let's try to make this twisty puzzle. The core of your puzzle is a Truncated rhombic dodecahedron. It has 6 square faces and 12 hexagon faces.

Image

To each of these faces you attach a fixed face center that can rotate. These can't be the 18 pieces on the Mixup Cube that you mention as they can change position relative to each other, these fixed ones can't. Still they could be floating face centers.

So the question becomes, can I find these floating face centers in the Face-Turning MultiTruncated Rhombic Dodecahedron?

Multi is used in the sense that it contains all the possible pieces that could be present in an Order=2 (two cut planes per axis of rotation) Twisty Puzzle based on this geometry. And yes that question could be answered using the exact same method I used here:

http://twistypuzzles.com/forum/viewtopic.php?f=1&t=15560

Create the cut planes that define your Truncated Rhombic Dodecahedron and allow the puzzle to grow till it approaches its deep cut (Order = 1) version (in this case that would be a combo of a 2x2x2 and a 24-Cube) and if none of the pieces in this twisty puzzle behave as your floating face centers on the Mixup Cube you've proven the Mixup Cube isn't a "normal" Twisty puzzle based on this geometry. I haven't done the leg work or I would show it here (I simply don't have the time at the moment or near future) but I really think you are going to run into problems. I'm about 99% sure your Mixup Cube's floating face centers do NOT exist is the pure Twisty Puzzle base on the geometry of a Truncated Rhombic Dodecahedron. I'd love to be proven wrong though.

Again if I'm following Matt's reasoning correctly you'd need an infinite number of axes of rotation. Ok... make the core a sphere. Now if your cut planes (2 per axis) contain any volume the infinite number of pieces in this puzzle don't have any volume to them. However there should be 18 zero volume pieces in the mix that DO behave as your Mixup Cube pieces.

So if (BIG IF as I haven't proven it) I'm correct the Mixup Cube could be considered a subset of this infinite axes of rotation pure Twisty Puzzle or it could be considered a Twisty/Slidey Puzzle.

Carl

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 Post subject: Re: Puzzles that jumble
PostPosted: Thu Jul 01, 2010 9:21 pm 
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I agree about battle gear just being bandaged. Also that brings up the question, can a twist on a puzzle be considered jumbled if only reversing the move to get it to the jumbled state allows it to be scrambled? Let's take a normal 3x3x3. If the top is rotated 10 degrees, only the top can be rotated. However, the cuts could be extended and form a jumbling puzzle. This is like the battle gear if it could jumble. One wheel is rotated blocking the other. Because the only move is to continue rotating the first wheel, should it even be considered bandaged?

With the mixup cube, glue the red center in place so every thing is relative to it. After any rotations on the puzzle, all axes of rotation are the same relative to the red center. They themselves may be in new locations but the 18 axes still form the same shape off of the red center.

This ties back to the top of my post. I would say the mixup cube cannot jumble because no rotations are blocked. The cuts can be extended to form a jumbling puzzle just like with my 3x3x3 example. However, because after rotating the top 45 degrees only that axis can continue rotating, I believe it is not bandaged or jumbled in any way.

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 Post subject: Re: Puzzles that jumble
PostPosted: Fri Jul 02, 2010 12:07 am 
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GuiltyBystander wrote:
It seems that the general consensus is that the Battle Gear jumbles despite having rational angles. I thought I would try to unbandage it a bit and see where the jumbling occurs. This is what I got.
Attachment:
battlegear.png


I stand corrected. My analysis was just plain wrong. Battle Gear does not, in fact, jumble.

That leaves the Split Hex as the simplest example of a jumbling puzzle which only has rational angles.


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