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 Post subject: Crazy 2-Face
PostPosted: Thu Mar 21, 2013 1:53 am 
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I like crazy puzzles. There is a sentimental attachment, since the mf8+dayan crazy planet cubes came out just as I was discovering twisty puzzles. Then the crazy tetrahedra came out, and they had faces with no circles. The Uranus version (0002) was particularly difficult. I still can't solve it. And that's because of the "2" face, with no circles.

Not too long ago, I decided that I needed some more crazy puzzles. So I made one. As expected, due to the extra 2 face, these things are HARD!

Then I made a kit, which contains all the pieces needed for all 26 of the (hopefully) unique variations I could find which needed one "2" face or two "2" faces. My only constraint was that each puzzle had to have at least one 2-face and at least one "0" face (otherwise the solving is trivial).

My only annoyance is that I wanted to make versions with three 2-faces. I had enough edges, but ran out of corners.

A few pics (please excuse photoshop misbehaving with some of the white edges)

Attachment:
crazy 2face solved.png
crazy 2face solved.png [ 541.76 KiB | Viewed 8551 times ]


Attachment:
crazy 2face checkerboard 1.png
crazy 2face checkerboard 1.png [ 559.11 KiB | Viewed 8551 times ]


Attachment:
crazy 2face checkerboard 2.png
crazy 2face checkerboard 2.png [ 660.06 KiB | Viewed 8551 times ]


When the cube has two "2" faces adjacent, it's especially hard to scramble.

Attachment:
crazy 2face scrambled.png
crazy 2face scrambled.png [ 608.71 KiB | Viewed 8551 times ]


I'm reasonably sure that I have all the possible unique variations and that I haven't doubled up on any. I took it as a "sign" that it was right, since there were 26. I named them appropriately. Below there's a chart showing them. The chart is done in the same way as the specification chart for the crazy planet cubes, and I view the yellow face as Back and white as Front.

Attachment:
crazy 2-face chart.jpg
crazy 2-face chart.jpg [ 217.23 KiB | Viewed 8551 times ]

Therre is some order to it.

A-F have one 2-face and have a "0" center opposite it.
G-K have one 2-face and have a "1" center opposite it.
L-P have two 2-faces adjacent and a "0" face opposite the yellow.
Q-U have two 2-faces adjacent and a "1" face opposite the yellow.
V-Z have two 2-faces opposite each other.

So, now I have 26 new puzzles. This should keep me busy. I'm very interested in anyone's opinion on the relative solving difficulty of these things. My feeling is generally that the more "0" faces, the harder.

Video here for those interested. :)

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Mar 21, 2013 2:45 am 
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Ooh my, 26 more Crazy 3x3x3.
This has to be called a systematic addiction :lol:
Now we expect 26 more videos, of course.

Welcome back in Crazy Village :lol:

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Mar 21, 2013 3:24 am 
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Hi rline,

nice idea ! I love crazy cubes.

Is the cube named "v" the crazy witeden super 3x3x3 ?

Cheers,
Andrea


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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Mar 21, 2013 4:42 am 
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Nice idea Rline,

Looks like we have some more fun crazy planet solving ahead :D .

I have 3 black circle planets that I had ready for a different mod, but I like yours better.. Looks like they will be sacrificed soon. Can you give us a diagram or photo of your kit to save some time? For example, if I have 3 Neptune Cubes what parts would I need to make, to make a `complete kit`?

Cheers,
Burgo.

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Mar 21, 2013 6:06 am 
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Fantastic Rline!

Now we need exact instructions in what we need to buy and how to do the conversions.

My only potential worry is that I do worry that unscrewing and re-screwing a puzzle 20 odd times will end up stripping the thread on them.

But this does look like a great project with at least another 26 videos for you! And me!

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Mar 21, 2013 1:11 pm 
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This is awesome man! Its a good thing you got me hooked on crazy circle cubes!


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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Mar 21, 2013 2:25 pm 
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Is this a bandaged crazy cube, or something more complex?

-Doug

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Mar 21, 2013 9:50 pm 
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Konrad wrote:
This has to be called a systematic addiction :lol:
Now we expect 26 more videos, of course.

Almost certainly not :lol:

Konrad wrote:
Welcome back in Crazy Village :lol:

Thankyou! it was nice to see the 3 member Crazytown committee to welcome me back (Konrad, Burgo, Andrea).

Andrea wrote:
nice idea ! I love crazy cubes.

Is the cube named "v" the crazy witeden super 3x3x3 ?

Very nice to hear from you again Andrea. I also love them. The "v" is actually the opposite of the witeden super 3x3x3. The witeden super 3x3x3 has 2 "0" faces and 4 "2" faces, whereas the V has 2 "2" faces and 4 "0" faces.

Burgo wrote:
Looks like we have some more fun crazy planet solving ahead :D .

I sure hope so. I was hoping others would be interested, because it's so much more fun solving (and getting stuck) with others than on your own.

Burgo wrote:
Can you give us a diagram or photo of your kit to save some time? For example, if I have 3 Neptune Cubes what parts would I need to make, to make a `complete kit`?

Puzzlemad wrote:
Now we need exact instructions in what we need to buy and how to do the conversions.

Yes. Next post when I work it out into something coherent.

Puzzlemad wrote:
My only potential worry is that I do worry that unscrewing and re-screwing a puzzle 20 odd times will end up stripping the thread on them.

Fair point. The good thing is there's a spare core and 6 spare screws, so that should help.

Hunter Palshook wrote:
This is awesome man! Its a good thing you got me hooked on crazy circle cubes!

Oh yeah. There's not much better than these crazy cubes.

Doug Roth wrote:
Is this a bandaged crazy cube, or something more complex?

I don't want to answer this one as I'll probably come across as having no idea what I'm on about. Burgo?

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Mar 21, 2013 10:16 pm 
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What a great idea rline. I too am a big fan of the crazy cube puzzles. The Saturn 3x3 is always in my notebook bag. Looking forward to hearing more details. As for a name for this set of puzzles, how about the crazy alphabet cubes?

I just can't resist asking, Is there a stickerless version? :lol:

Wait a minute, I just glanced over at my crazy megaminx puzzles. Hmmm....


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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Mar 21, 2013 10:46 pm 
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ft38 wrote:
What a great idea rline. I too am a big fan of the crazy cube puzzles. The Saturn 3x3 is always in my notebook bag. Looking forward to hearing more details. As for a name for this set of puzzles, how about the crazy alphabet cubes?

Thanks!
Oh your name for the puzzles is so good! I'm good with that, as long as someone confirms there are definitely 26, no more, no less.

ft38 wrote:
I just can't resist asking, Is there a stickerless version? :lol:

I wish there was. :? I could only really make these because of the fact that they were in black plastic. So that was a plus. But I hate these little stickers. I miss the coloured plastic.

KEY POINT!
What we need is for Calvin to produce and sell us a coloured plastic DIY kit of the crazy alphabet cubes! It wouldn't be hard.

ft38 wrote:
Wait a minute, I just glanced over at my crazy megaminx puzzles. Hmmm....

It does open up a number of possibilities, but I can only imagine how tedious the 2-face megaminxes might be...

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 Post subject: Re: Crazy 2-Face
PostPosted: Fri Mar 22, 2013 1:35 am 
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Hey rline, can you elaborate on what "2-face" and "0-face" mean?

From your diagram it seems like there are faces with circles, faces with hollow circles, and faces without circles. Which are what?

For example, what's the difference between T-011221and F-110121 in your chart?

If there are 3 unique face types then there are 57 distinct ways to make a cube with them and if you count identical mirrors as the same puzzle (they solution is essentially the same) then only 56 ways.

See http://twistypuzzles.com/forum/viewtopic.php?p=295505#p295505 and http://oeis.org/A198833

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 Post subject: Re: Crazy 2-Face
PostPosted: Fri Mar 22, 2013 1:59 am 
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Hey Brandon

bmenrigh wrote:
can you elaborate on what "2-face" and "0-face" mean?

Sure. If you look at the original (official specification) put out by mf8 when they released the crazy planet cubes...

Image

they called the earth "11", designating the white and green faces where the center parts did turn with the face as "1" faces. And the other faces were "0", indicating the center parts did not turn with the face. The faces with circles with diagonals through them are "0" faces, those with hollow circles are the "1" faces.

Then, when they released the crazy tetrahedra, and had faces with no circles...

Attachment:
crazy planet tetrahedra.jpg
crazy planet tetrahedra.jpg [ 35 KiB | Viewed 8138 times ]


you'll see they do a similar thing, but then designate the faces with no circles as "2" faces.

So I've done the same thing with the crazy 2-face puzzles.

Quote:
For example, what's the difference between T-011221and F-110121 in your chart?

So T has two "2" faces (faces without circles) whereas F has only one "2" face. Also, the arrangement of "0" and "1" faces is different. What I mean by this is that each diagram has a red face which is Up, then it goes LFRB, and finally the Down face at the bottom. So on F, the "0" face is opposite the "2" face, whereas on T, the '0" face is adjacent to it/them.

Quote:
If there are 3 unique face types then there are 57 distinct ways to make a cube with them and if you count identical mirrors as the same puzzle (they solution is essentially the same) then only 56 ways.

Welll, firstly, my stipulation (in my 1st post) was that each cube had to have at least one "0" face and at least one "2" face, to ensure the solve wasn't just a standard rubik's cube solve. (If there are no "0" faces, the circle parts can't break away from their pieces) So that discounts some.

Secondly, there are versions which can be made which have three "2" faces, and four "2" faces, and five "2" faces, but it's not possible to make them from two physical puzzles. This annoyed me! To get another few puzzles, I was two corners short :twisted: and due to the mechanism of the crazy circle puzzles, I couldn't just shove in some normal corners from another puzzle. I'm still thinking about trying to modify a normal corner, but it'll take a little work, and I wanted this to be a self-contained kit.

Also, even though a puzzle like B-000120 might be theoretically different from a puzzle such as 000021, in practice they're the same puzzle. This is because the only change there is to move the "1" face from the green face to the red face, which doesn't change the puzzle or the solving experience.

Every fibre of my being hopes you can prove to me (and others) that there are somewhere closer to 57 puzzles to make, but I think 26 might be the limit.

I hope all this makes sense. If not, get me to clarify further.

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 Post subject: Re: Crazy 2-Face
PostPosted: Fri Mar 22, 2013 2:38 am 
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rline wrote:
Doug Roth wrote:
Is this a bandaged crazy cube, or something more complex?

I don't want to answer this one as I'll probably come across as having no idea what I'm on about. Burgo?
It's just that really.. a `bandaged crazy cube`. Crazy Cubes are already a bandaged circle cube, so with a bandaged, bandaged cube there is an additional challenge. The idea of making a 2 face (as Rline has already pointed out) has already been explored in the Tetrahedrons, in which, commercially, the puzzles were probably either too easy or too hard, never just right, in any case I didn't particularly like them much. But in the 333 form, the Witeden Super333 was very interesting as a bandaged Crazy Cube. I am hopeful that these won't be as difficult as the Tets, because there are more faces they might be more interesting. It's a great idea to reverse engineer the Tets back to the 333s. And for the price (of potentially 3 crazy cubes) it's a reasonable thing to do, a very easy mod too. Kevin, in my experience you will need new stickers before you will need a new core.

Cheers,
Burgo.

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 Post subject: Re: Crazy 2-Face
PostPosted: Fri Mar 22, 2013 5:53 am 
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How to make the Crazy 2-Face kit

[This uses the colour scheme I decided on. Of course, any colour scheme is fine, but if you do a different one, you'll have to adjust the colours below. Also, it would be good if anyone else did make the kit if we were all using the same colour puzzles.]

Ingredients

1) Two black plastic crazy 3x3x3 plus planet cubes which give you a total of 6 "0" centers and 6 "1" centers. Get them unstickered or you will need lots more sticker material.

Examples:

* Jupiter+Mercury
* Earth+Uranus
* Neptune+Mars
* Saturn+Venus
* Neptune+Neptune
* Mars+Mars

2) Superglue
3) Wet and dry sandpaper (something like 120,240,400 and maybe 800)
4) Sticker material or leftover stickers measuring around 1.6cm x 1.6cm (colours explained later)
5) Milliput or other epoxy putty
6) Something to polish the plastic, eg. car scratch remover polish, vegetable oil, black texta

Method

1. After pulling apart the pieces of the 2 puzzles, superglue and milliput the following

1 x main (RC) edge + 2 circle edge pieces
11 x main (RC) edge + 1 circle edge pieces
2 x main corner + 2 circle corner pieces
10 x main corner + 1 circle corner pieces

Once dry, sand down and polish up to your level of happiness.

Now, sticker the edges as follows. Capital letters indicate the glued piece:

YELLOW/GREEN [this is the edge with 2 circle edges glued to it]
YELLOW/orange [this means to use a full square sticker for the yellow side of the edge, and the two separate circle edge stickers for the orange side of the edge]
YELLOW/blue
YELLOW/red
YELLOW/green
WHITE/green
WHITE/orange
WHITE/blue
WHITE/red
GREEN/orange
GREEN/red
GREEN/white
white/orange
white/blue
white/red
white/green
orange/blue
blue/red
red/green
green/orange

You should now have 4 edges left over.

Sticker the corners as follows. It's crucial to make sure the colours are correct in terms of the direction also, as you don't want to end up with a corner that doesn't fit, colourwise. So, I am stickering clockwise around the corner.

GREEN/YELLOW/orange [this means to use a full square sticker for green, then go clockwise, and use a full square sticker for yellow, and finally use the two separate circle corner stickers for the orange]
GREEN/red/YELLOW
YELL/blue/orange
YELL/red/blue
YELL/green/red
YELL/orange/green
GREEN/orange/white
GREEN/white/red
WHITE/orange/blue
WHITE/blue/red
WHITE/red/green
WHITE/green/orange
white/orange/blue
white/blue/red
white/red/green
white/green/orange

You should have no remaining corners.

At this point, all required pieces should be stickered, and you should have 6 "0" center pieces and 6 "1" center pieces. You'll have a spare core+6 screws, and a spare 4 edges.

Now you can make all 26 puzzles in the set.

In case it helps, here's a picture of the centers and the pieces which end up glued in some way, along with their accompanying circle parts. Note: this doesn't show every piece required; just the bits that have been modified.

Attachment:
glued pieces.png
glued pieces.png [ 251.64 KiB | Viewed 8047 times ]


Here's a video showing the process I used to make them. Note that it's assuming the viewer knows basically nothing about this, so please don't feel patronised if it seems obvious. It's 46 minutes, because it goes through the whole process. However, this is only for making the single 2-face cubes.

And lastly, if anyone wants a kit but doesn't have the time, inclination or confidence to make one, PM me and I'll make one for you (with a small profit for my retirement fund :lol: )

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Last edited by rline on Fri Mar 22, 2013 3:38 pm, edited 1 time in total.

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 Post subject: Re: Crazy 2-Face
PostPosted: Fri Mar 22, 2013 6:11 am 
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Great idea, one of the best forms of bandaging I have seen. Must be very tough to solve, almost like the latch cube! :shock: :D

And I LOVE the name!!! :lol:

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 Post subject: Re: Crazy 2-Face
PostPosted: Fri Mar 22, 2013 6:30 am 
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KelvinS wrote:
Great idea, one of the best forms of bandaging I have seen. Must be very tough to solve, almost like the latch cube! :shock: :D

Thanks Kelvin :) When I thought of it, I hoped it would turn out well! My feeling, having solved 5 so far, is that the easiest ones will be slightly harder than the easier crazy planet cubes, and the hardest ones will be much harder than the latch cube. In fact, I think I'll have no real idea how to solve the ones like A or L. I think V will be slightly easier than L but it's a guess.

Quote:
I'm not sure why you have some circles drawn with a cross (X), and some with a plus (+), how are they different?

Ah, that's because some faces (with a cross) have the inside circle parts which stay fixed when you turn the face, whereas others (with a plus) have the inside circle parts which turn with the face. See my answer to Brandon above a few posts for more of an explanation.

Perhaps some folks will start to understand why we crazy people get so excited about the crazy planets and tetrahedra and megaminxes etc, and why we feel so sorry for people who have never played with a crazy planet cube. :lol:

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 Post subject: Re: Crazy 2-Face
PostPosted: Fri Mar 22, 2013 5:51 pm 
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rline wrote:
Every fibre of my being hopes you can prove to me (and others) that there are somewhere closer to 57 puzzles to make, but I think 26 might be the limit.

Alright I hacked up some code to check this. The constraint is that the puzzle must have at least one 0-face and one or two 2-faces.

There are 25 configurations if you count mirror states as different. Since mirrored configurations solve the same way, there are only 24 essentially unique versions.

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 Post subject: Re: Crazy 2-Face
PostPosted: Fri Mar 22, 2013 6:10 pm 
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I think O and R are the same configuration, but what's the other set of doubles?

I thought of bandaging some 2-faces on my circle cubes too, but decided to first solve the eight regular variants, which is proving to take long...

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 Post subject: Re: Crazy 2-Face
PostPosted: Fri Mar 22, 2013 6:42 pm 
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Okay I manually entered the configs.

001220 is a dup with 010220 under normal reorientation.

001221 is a dup with 010221 under mirroring + reorientation.

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 Post subject: Re: Crazy 2-Face
PostPosted: Fri Mar 22, 2013 6:52 pm 
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bmenrigh wrote:
There are 25 configurations if you count mirror states as different. Since mirrored configurations solve the same way, there are only 24 essentially unique versions.

Well that's no good. We'll need to throw out a couple of the letters of the alphabet. :shock:

bmenrigh wrote:
Okay I manually entered the configs.

001220 is a dup with 010220 under normal reorientation.

001221 is a dup with 010221 under mirroring + reorientation.

Ok. I agree. Damn. :twisted: I was sure it had to be 26.

Well, I've solved a few of them (all the ones with only one "0" face and a couple with two "0" faces), and it occurred to me that perhaps a better way of ordering the set might be by number of "0" faces, progressing from one "0" face through to 5.

Any thoughts from anyone on this, or anything else? I'll end up making a new chart anyway because I won't be happy having rogue duplicate puzzles on there.

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 Post subject: Re: Crazy 2-Face
PostPosted: Fri Mar 22, 2013 11:47 pm 
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I've just started making mine. Seeing as I have 3 puzzles I decided to go with a few more face possibilities. The only ones I can't get to with 3 cubes are the Witeden Super333 which I have anyway and the 0,1 configuration of the same puzzle, but I have the early Witeden Super335 and if I'm not mistaken the challenge is within that.

Don't forget the options to bandage a 2 face so that it cannot move.. interestingly if all circle pieces surround one of these type of faces it will twist.

My configuration is using Rline's YGW faces to make the `linear 3 faces`, and then Orange as the third dedicated 2 face colour to surround the YGO corner, WYGO as the 4 faces, the linear 4 faces would include YGWB (but I need another 4 corners to make them). Hopefully, like he said, if we can have consistent colour schemes it would make it easier, so I made a table for what I did:

Pieces list for 3 puzzles (capitals designate bandaging):
Bandaged Edges: Yg Yo Yr Yb Wg Wo Wr Wb Gw Go Gr Ow Ob GY GW GO YO WG WO
Bandaged Corners: Ygo Yrg Yrb Yob Wgo Wrg Wrb Wob Gow Grw Obw YGo YGr GOw OYb GWo GWr WOb GOY GOW
Unbandaged Edges: go gr rb ob wb ow gw rw
Unbandaged Corners: wgo wgr wbr wob
Unbandaged inner edges: 4xea of gowrb
Unbandaged CCs: 4xea of gowrb
for the 4th puzzle (to include all possibilities): WBo WYo WBr YBr WB YB Bo Br

I hope I've got all that correct.
Cheers,
Burgo.

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 Post subject: Re: Crazy 2-Face
PostPosted: Sat Mar 23, 2013 7:45 am 
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Silly me, I was just working on the pieces and started pulling them apart to clean out some polish and it occurred to me that the corners and edges come apart so easily that all you really need is 2 cubes to make a whole set for every combination possible. You will just need to disassemble the edges and corners to make the different piece types. They are much easier to do this with than the original coloured puzzles.

Also to answer Kevin's question about the core more thoroughly, the core can be easily replaced with a standard 333 core like: http://www.hknowstore.com/locale/en-US/ ... d5aee94e36 I have about 3 types lying around and they all fit.

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 Post subject: Re: Crazy 2-Face
PostPosted: Sat Mar 23, 2013 4:26 pm 
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Burgo wrote:
Silly me, I was just working on the pieces and started pulling them apart to clean out some polish and it occurred to me that the corners and edges come apart so easily that all you really need is 2 cubes to make a whole set for every combination possible. You will just need to disassemble the edges and corners to make the different piece types. They are much easier to do this with than the original coloured puzzles.

You better explan this Burgo. :? Are you saying that after gluing and milliputting the pieces, it's easy to pull them apart to make all the combinations? What about stickers? I'm sure I've not understood what you're saying...

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 Post subject: Re: Crazy 2-Face
PostPosted: Sat Mar 23, 2013 4:47 pm 
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He's saying that the actual corner pieces and edge pieces (not the circle bits) can be dismantled easily, just like say the pieces in the crazy tetrahedra, so you can then assemble them to make various combinations, such as one side with, and two sides without circles for a particular corner piece - you don't need to have the corners and edges for every possible combination premade.

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 Post subject: Re: Crazy 2-Face
PostPosted: Sat Mar 23, 2013 4:57 pm 
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After gluing and milliput: You will only ever need 4 bandaged edge & corner halves of each colour, and 4 unbandaged edge & corner halves of each colour. Now the problem with this might be that after a time the grip of the piece halves might not be as good? They come apart just by putting your fingernail into the gap and pressing. They are different to the originals, the corners are obviously incompatible, but the edges are incompatible as well. I have included a picture of the core with a C4U core inserted. EDIT, yes Marty :)


Attachments:
Crazy 333 Parts.jpg
Crazy 333 Parts.jpg [ 1.93 MiB | Viewed 7653 times ]

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 Post subject: Re: Crazy 2-Face
PostPosted: Sat Mar 23, 2013 6:07 pm 
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Rline, this is such an awesome succcess!


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 Post subject: Re: Crazy 2-Face
PostPosted: Sat Mar 23, 2013 6:13 pm 
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Quote:
He's saying that the actual corner pieces and edge pieces (not the circle bits) can be dismantled easily, just like say the pieces in the crazy tetrahedra, so you can then assemble them to make various combinations, such as one side with, and two sides without circles for a particular corner piece - you don't need to have the corners and edges for every possible combination premade.

Oh right. i get it now. So just the same as I ended up doing to make all the tetrahedra out of one of them a couple of months back. Now I feel silly...

So, for someone like me who's already "made" and used up all 16 corners and all but 4 of the edges using the colour scheme set out by me and then Burgo, is there a clear set of instructions for how I can pull apart which pieces where in order to get all the combinations? Or is it too late?

[I do actually have a 3rd crazy planet puzzle, but I'd prefer to keep it for a different mod...]

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 Post subject: Re: Crazy 2-Face
PostPosted: Sat Mar 23, 2013 6:29 pm 
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You need:
4x6=24 unbandaged pieces of `everything`: Corner halves, Edge halves, CCs & Inner Edges. Stickered in every colour X4.
4x5=20 bandaged pieces of `everything` : Corner halves + CCs & Edge halves + Inner Edges. Stickered in every colour X4, except 1 (I initially chose red in my scheme above^^, but I think I'll do red for the sake of completeness.

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 Post subject: Re: Crazy 2-Face
PostPosted: Sat Mar 23, 2013 7:21 pm 
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There are so many possibilities here (I got to thinking what I might do with my leftover and half made pieces):

The opportunity to bandage a 2 face so that it cannot move (unless all circle pieces surround one of these type of faces it will twist) as I suggested above^^. Maybe we could call the `locked 2 faces` 3 faces? This would give 0, 1, 2 & 3 face types. It would occur when you use `2-face edge & corner pieces` and a `0-face centre piece`.

The opportunity to combine this with traditional bandaging on a Crazy 333: Like in the CT bandaged 333 thread, but we could bandage anything together, CCs >< Inner Edges, Unbandaged Corners >< Unbandaged Edges, Bandaged Edges >< Bandaged Corners, Half Bandaged Edges >< Partly Bandaged Corners, Clocked Centres >< Inner Edges, Inner + Outer Edges, faces with combinations of bandaging. All of the possibilities for combinations of 0, 1, 2 & 3 faces with traditional bandaging are almost limitless. So we would have a bandaged Circle Cube, with bandaged 2 faces, bandaged 3 faces, and then bandaged traditionally :) .

I’m sure we’ll get some good puzzles out of those!
Cheers,
Burgo.

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 Post subject: Re: Crazy 2-Face
PostPosted: Sat Mar 23, 2013 11:53 pm 
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Quote:
I’m sure we’ll get some good puzzles out of those!

Well my head is spinning and I feel like I've kickstarted a runaway train. Now, who will list all the possible puzzles able to be made from what Burgo suggested? It won't be me! :lol:

Also, now that there are many more possibilities, we need a better naming system for each puzzle, but also for the whole set. I implemented the 1st prototype, Burgo came along and improved it. We're both Australian. I vote for "The Aussie Cube"! :P

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 Post subject: Re: Crazy 2-Face
PostPosted: Sun Mar 24, 2013 5:42 am 
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I finished making my Crazy 2 Face set, and I made a few slightly more traditionally bandaged pieces as well which I'll show:
Attachment:
Small Bandage Set.jpg
Small Bandage Set.jpg [ 756.06 KiB | Viewed 7644 times ]

I think I might name the 4th type of Crazy bandaging B4? So we have O, 1, 2, 3 & B4.
Attachment:
Crazy B4 Cube.jpg
Crazy B4 Cube.jpg [ 929.53 KiB | Viewed 7644 times ]

The featured puzzle is only for an example of the kinds of bandaging that are possible. I don't care too much for presenting, I just want to share my ideas, obviously Rline's Crazy 2-Face inspired it, but for the sake of it.. I'll call it the `Crazy B4 Cube`.

EDIT: I just read Rline's post about naming things.. I have no idea how to go about naming everything. The Crazy 2-Face lends itself to a table, but further bandaging probably needs photographic presentation like in the CT bandaged 333 thread (along with face numbering like: [Y0, R1, G3, O2, B0, W0]).

EDIT 2: I just managed to thoroughly scramble the example cube ^^. At first I didn't think it was fully scramblable. It would be a very tough puzzle if anyone wishes to attempt it (I think it might be interesting to put it together in the scrambled situation to see what you think of it too?):
Attachment:
Fully scrambled B4 example cube.jpg
Fully scrambled B4 example cube.jpg [ 688.3 KiB | Viewed 7305 times ]
The Centres pattern is [Y0(0), G0(0), R0(0), W1(+), O2(+), B3(0)].

Cheers,
Burgo.

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Last edited by Burgo on Wed Mar 27, 2013 5:38 am, edited 2 times in total.

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 Post subject: Re: Crazy 2-Face
PostPosted: Sun Mar 24, 2013 5:45 am 
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Trust you Burgo! Take an insanely difficult set of puzzles... and make them harder :D

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 Post subject: Re: Crazy 2-Face
PostPosted: Sun Mar 24, 2013 5:56 am 
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Yeah, I'd say the example has too many incidents of bandaging, it's only an example :) . I think the better ones will have only 1 or 2 B4 bandagings. Maybe I'm wrong?

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 Post subject: Re: Crazy 2-Face
PostPosted: Sun Mar 24, 2013 6:48 am 
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Well I'm sure there are a whole lot of possibilities, ranging from the easier side of things to the harder, much like the bandaged 3x3 thread we had. I just meant that these crazy puzzles with 2 type faces are already very difficult I'm sure, and your first thought before solving them seems to be 'hmm...how can I make these even more difficult?' :lol:

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 Post subject: Re: Crazy 2-Face
PostPosted: Sun Mar 24, 2013 5:57 pm 
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martywolfman wrote:
Well I'm sure there are a whole lot of possibilities, ranging from the easier side of things to the harder, much like the bandaged 3x3 thread we had. I just meant that these crazy puzzles with 2 type faces are already very difficult I'm sure, and your first thought before solving them seems to be 'hmm...how can I make these even more difficult?' :lol:

Marty, I can guarantee you that (from PMs) Burgo's 1st thought is definitely "How can I make this harder?" :lol:

martywolfman wrote:
I just meant that these crazy puzzles with 2 type faces are already very difficult I'm sure

I concur. I've been playing with a few variants. Essentially, the puzzles are the planet puzzles with some extra 2-faces. So for example, puzzle O is a uranus cube with two 2-faces. So I made it up and started by trying to make the red-white complete edge, as I would for the standard uranus. This is the 1st step in a reduction solve, and on uranus it's a matter of seconds. So far, I haven't been able to do it. Why? because the two 2-faces mean I just can't turn my required faces without a million 2-face pieces stopping me from doing it. It's disheartening :lol: I mean, either I'll have to figure out a way of putting all those pieces right out of the way and keeping them out of the way, or else come up with some new way of solving this puzzle. I think this may be where a lot o the challenges lie. Initially I thought the 2-face pieces might just make things more tedious, but for me at least, this is an example of it changing things entirely.

I still think A will be the hardest of the lot.

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 Post subject: Re: Crazy 2-Face
PostPosted: Mon Mar 25, 2013 7:00 pm 
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Is the six 2-Face (i.e. a 3x3 cube) a trivial member of the Aussie Planets?

Will HKNowStore send them unstickered and if not, who will?

This is a great idea that keeps getting better every time I read this thread. 8-)

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 Post subject: Re: Crazy 2-Face
PostPosted: Mon Mar 25, 2013 7:10 pm 
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Pete the Geek wrote:
Is the six 2-Face (i.e. a 3x3 cube) a trivial member of the Aussie Planets?

Will HKNowStore send them unstickered and if not, who will?

This is a great idea that keeps getting better every time I read this thread. 8-)

Yes the six 2-face is a trivial member. For that matter, so is the five 2-face. Even if the 6th face on that one is a "0" face, it can't be scrambled apart from a single turn. So really, the challenges lie in the one, two, three and four 2-faces, as well as all the other options Burgo has explained.

HKnowstore sent the puzzles to me unstickered (without me asking) so I suspect they'd do that for anyone else.

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Mar 27, 2013 5:46 am 
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For those interested, I just edited my post above^^ with pictures of the example Crazy B4 Cube fully scrambled. I also put the Centres pattern in the post so it's possible to replicate the puzzle. The interesting thing is that I only made it to show off the pieces, but it turns out to be a really diffficult and fully scramblable puzzle. Can anyone pick the 2 pieces that actually can't be scrambled?

Cheers,
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 Post subject: Re: Crazy 2-Face
PostPosted: Tue Apr 02, 2013 12:18 pm 
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rline wrote:
bmenrigh wrote:
There are 25 configurations if you count mirror states as different. Since mirrored configurations solve the same way, there are only 24 essentially unique versions.

Well that's no good. We'll need to throw out a couple of the letters of the alphabet. :shock:


May I suggest Crimean Tatar, Leonese, Maltese, Pan-Nigerian, Swahili, Uzbek or Volapük alphabet? They are all Latin based and have exactly 24 letters each.

When you make and solve the different combinations, would you mind listing them in order of difficulty? I'd like to make one (and it would be possible to make one of your crazy 2-faces using only a single crazy planet, right?) but I probably want one of the easiest.

And I was thinking, wouldn't it be even more challenging if you spread out the cut pieces so that no side has a complete circle in the solved state? Though I suppose this would take away the pleasure of having a complete set, with manageable size, of possible puzzles.


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 Post subject: Re: Crazy 2-Face
PostPosted: Tue Apr 02, 2013 8:15 pm 
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Quote:
When you make and solve the different combinations

Well, for me at least, I probably won't be doing this. Something else (non TP-related) has come up which will mean I won't really be able to contribute to this all that much from here on in.

Quote:
would you mind listing them in order of difficulty?

I think essentially it depends on the base planet and the method you use. Eg. using reduction, I found the order of difficulty to be something like jupter, uranus, mercury, earth, venus, neptune, mars, saturn. Putting an extra 2-face or two on the puzzles generally means it'll increase the difficulty. I've solved a few of the easier ones and found this. I stll think 000002 will be the hardest, and this was the one that originally inspired the idea of it, following the 0002 uranus tetrahedron.

Quote:
and it would be possible to make one of your crazy 2-faces using only a single crazy planet, right?) but I probably want one of the easiest

then I'd make F. I think that one is the easiest.

Quote:
And I was thinking, wouldn't it be even more challenging if you spread out the cut pieces so that no side has a complete circle in the solved state?

Definitely. I think that was what Burgo was doing above.

Quote:
Though I suppose this would take away the pleasure of having a complete set, with manageable size, of possible puzzles.

Have a good look through Burgo's posts in this thread. He has given instructions of how to make every combination you could want using just 2 puzzles.

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Apr 03, 2013 6:58 am 
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I tried Jupiter, with one added 2 face adjacent to the 0 face, so 021111 I guess. I'm still waiting for the sandpaper I ordered to arrive, so I just put it together with a black face so I havent tried much of this yet, but that puzzle was extremely easy, once you can solve the crazy Jupiter, it didn't add a great deal to the solve really, other than keeping the 2 pieces away from the 0 face.

rline wrote:
I stll think 000002 will be the hardest, and this was the one that originally inspired the idea of it, following the 0002 uranus tetrahedron.



Whilst I bow to your far superior twisty puzzle knowledge and solving ability, and I haven't tried this yet, I'm not convinced that this is entirely correct. I think that the difficulty (although I haven't tried it that much) of this and the other crazy tetrahedrons is based on the fact that there is very little you can do in terms of turning that doesn't put a 2 piece on a zero face, making it impossible to turn. With a 000002 cube you've more space to put the 2 pieces to keep them out of the way, and it's not so difficult to keep the 2 pieces on one face out of the way I think, say at the back of the puzzle while you solve the rest I would expect something like 000022 or 000222 (If you are prepared to go to 3 type 2 faces) to be a lot harder, simply because there are more 2 pieces floating around that would get in the way.

What do you think?

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Apr 03, 2013 8:02 am 
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Then again, 000222 has three faces that will always turn.

Are there any 3x3s whose pieces would fit together with the circle cubes? If so, that would be awesome.

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Apr 03, 2013 3:17 pm 
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martywolfman wrote:
I tried Jupiter, with one added 2 face adjacent to the 0 face, so 021111 I guess. I'm still waiting for the sandpaper I ordered to arrive, so I just put it together with a black face so I havent tried much of this yet, but that puzzle was extremely easy, once you can solve the crazy Jupiter, it didn't add a great deal to the solve really, other than keeping the 2 pieces away from the 0 face.

rline wrote:
I stll think 000002 will be the hardest, and this was the one that originally inspired the idea of it, following the 0002 uranus tetrahedron.



Whilst I bow to your far superior twisty puzzle knowledge and solving ability, and I haven't tried this yet, I'm not convinced that this is entirely correct. I think that the difficulty (although I haven't tried it that much) of this and the other crazy tetrahedrons is based on the fact that there is very little you can do in terms of turning that doesn't put a 2 piece on a zero face, making it impossible to turn. With a 000002 cube you've more space to put the 2 pieces to keep them out of the way, and it's not so difficult to keep the 2 pieces on one face out of the way I think, say at the back of the puzzle while you solve the rest I would expect something like 000022 or 000222 (If you are prepared to go to 3 type 2 faces) to be a lot harder, simply because there are more 2 pieces floating around that would get in the way.

What do you think?

What do I think? I welcome the opinion. I asked more than once above in the thread for people's opinions on difficulty but don't think anyone took that up. Thanks for contributing! :) On reading what you wrote, I'd say I probably agree with you.

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Apr 04, 2013 9:43 am 
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Yeah, I'm not the best at judging the difficulty of these things before I start playing with them :D

I was waiting until I got them made before I did any real comments. I now have a couple of proper faces done, sanded and stickered now. I plan to do a couple more. I have 3 of these puzzles, so I can make several different variations at the same time.

So far as I mentioned above I've made the Jupiter with one added 2 face adjacent to the white 0 face, which was a relatively trivial solve, if you can solve Jupiter, you can solve that. I plan to try it with 2 type 2 faces later. Whilst making a Mercury in the same format - a type 2 Face adjacent to the white 1 face. I haven't tried it yet, but I will later today. However, having to swap the centre over from a 1 face, so that the 2 face would turn, also made me come accross another possibility, I guess I'd call it a type 3 face. The 0 centre, with type 2 pieces surrounding it, of course make a face that cannot turn, so it's almost like of of those constrained cubes, a completely blocked face (unless you populate it with circle pieces of course) I think that will add an interesting variation to the puzzles too, having faces that are unable to turn.

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Apr 10, 2013 4:26 pm 
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Well, I've been playing around with a few of these this week, they are definitely fun! I've mostly been doing variations on the jupiter version so far. With just one type 2 face, its trivially different to the regular Jupiter, with 2 type 2 faces its still not much different. However adding a type 3 face as I mentioned in my last post definitely spices things up a bit.

With one type 2 face and one type 3 face, adjacent to each other, and both adjacent to the white, 0 face, it definitely adds some difficulty. It's not horrendously difficult, I solved it, which says a lot :lol:

I'm currently working on this one, which is giving me problems:
Attachment:
type2.jpg
type2.jpg [ 12.5 KiB | Viewed 6632 times ]


The yellow face is the type 3 face, so no circle, but a fixed centre. I'm struggling with this one. I've got all the edges and corners reduced, but that took me a while. I can't get it solved at the moment without messing the paired pieces up though. A WIP this one :)

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Apr 10, 2013 5:10 pm 
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bmenrigh wrote:
rline wrote:
Every fibre of my being hopes you can prove to me (and others) that there are somewhere closer to 57 puzzles to make, but I think 26 might be the limit.

Alright I hacked up some code to check this. The constraint is that the puzzle must have at least one 0-face and one or two 2-faces.

There are 25 configurations if you count mirror states as different. Since mirrored configurations solve the same way, there are only 24 essentially unique versions.
Adding a 4th face type using martywolfman's "type 3" non-turning faces like so:

Image

Yields more interesting results. There are 220 possible configurations using 4 different face types. Here is a breakdown for each type:
Code:
# type-0   # type-1   # type-2   # type-3   ->    Count
0006 -> 1
0015 -> 1
0024 -> 2
0033 -> 2
0042 -> 2
0051 -> 1
0060 -> 1
0105 -> 1
0114 -> 2
0123 -> 3
0132 -> 3
0141 -> 2
0150 -> 1
0204 -> 2
0213 -> 3
0222 -> 5
0231 -> 3
0240 -> 2
0303 -> 2
0312 -> 3
0321 -> 3
0330 -> 2
0402 -> 2
0411 -> 2
0420 -> 2
0501 -> 1
0510 -> 1
0600 -> 1
1005 -> 1
1014 -> 2
1023 -> 3
1032 -> 3
1041 -> 2
1050 -> 1
1104 -> 2
1113 -> 4
1122 -> 6
1131 -> 4
1140 -> 2
1203 -> 3
1212 -> 6
1221 -> 6
1230 -> 3
1302 -> 3
1311 -> 4
1320 -> 3
1401 -> 2
1410 -> 2
1500 -> 1
2004 -> 2
2013 -> 3
2022 -> 5
2031 -> 3
2040 -> 2
2103 -> 3
2112 -> 6
2121 -> 6
2130 -> 3
2202 -> 5
2211 -> 6
2220 -> 5
2301 -> 3
2310 -> 3
2400 -> 2
3003 -> 2
3012 -> 3
3021 -> 3
3030 -> 2
3102 -> 3
3111 -> 4
3120 -> 3
3201 -> 3
3210 -> 3
3300 -> 2
4002 -> 2
4011 -> 2
4020 -> 2
4101 -> 2
4110 -> 2
4200 -> 2
5001 -> 1
5010 -> 1
5100 -> 1
6000 -> 1


Where "2310 -> 3" means that there are three configurations with two 0-type faces, three 1-type, one 2-type, and zero 3-type faces.

rline's 24 configurations are the sum of:
Code:
1320 -> 3
1410 -> 2
2220 -> 5
2310 -> 3
3120 -> 3
3210 -> 3
4020 -> 2
4110 -> 2
5010 -> 1


It seems like the next most interesting criteria would be at least one 0-type, exactly one 3-type, and one or two 2-type faces. This is basically rline's criteria but adding a 3-type face. There are 31 unique configurations:
Code:
1221 -> 6
1311 -> 4
2121 -> 6
2211 -> 6
3021 -> 3
3111 -> 4
4011 -> 2

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Apr 11, 2013 1:02 am 
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It'd be nice if we read the thread guys. I was talking about the 3 face (and I even called it that too) and a number of other things quite early on. Not that I want to brag, or lay claim to things, it's just nice to feel that what you contribute actually gets read :) .

Cheers,
Burgo.

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1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Apr 11, 2013 5:15 am 
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Argh, sorry burgo, I probably did read it, I'm sure I read the whole thread at some point but forgot about it before posting. That's maybe even where I subconciously got the idea

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Apr 11, 2013 6:30 am 
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No problem Marty, it’s just one of the things that happens in threads. Funny how we both independently thought to call it the 3 face.

And thanks to Brandon for the legwork on the analysis.. I think you’re right: `exactly one 3-face` is the most interesting, because if you have 2 3-faces: If the 3-faces are adjacent, then there is an unmovable edge wedged between them, and also (therefore) you can never make a turnable 0-face out of either of them during the scramble/solve. If the 3-faces are opposite then it negates this, but there are limited cases of this, however, they could be interesting because they fit the Saturn format.

Personally, I’ve had my puzzle set up as my `crazy B4 example cube` and been pondering solving that, but it’s fantastically difficult, and I think I might photograph it in its current state and come back to it another day because there are too many 2-face puzzles to have fun with first.

Cheers,
Burgo.

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1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Sep 18, 2013 1:12 pm 
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After counting by Polya Enumerations in combinitorics.

If 3 types are allowed for each face, then there are 57 cases.
The generating function is:
Code:
a^6+a^5*b+a^5*c+2*a^4*b^2+2*a^4*b*c+2*a^4*c^2+2*a^3*b^3+3*a^3*b^2*c+3*a^3*b*c^2+2*a^3*c^3+2*a^2*b^4+
3*a^2*b^3*c+6*a^2*b^2*c^2+3*a^2*b*c^3+2*a^2*c^4+a*b^5+2*a*b^4*c+3*a*b^3*c^2+3*a*b^2*c^3+2*a*b*c^4+a*c^5+
b^6+b^5*c+2*b^4*c^2+2*b^3*c^3+2*b^2*c^4+b*c^5+c^6


'a' means Type-0
'b' means Type-1
'c' means normal face.
The term '3*a^3*b^2*c' means there are 3 cases for 3 a's, 2 b's and 1 c's.

Suppose there must be at least 1 a's and 1 c's, then there are 38 cases.
The generating function is:
Code:
a^5*c+2*a^4*b*c+2*a^4*c^2+3*a^3*b^2*c+3*a^3*b*c^2+2*a^3*c^3+3*a^2*b^3*c+6*a^2*b^2*c^2+3*a^2*b*c^3+2*a^2*c^4+
2*a*b^4*c+3*a*b^3*c^2+3*a*b^2*c^3+2*a*b*c^4+a*c^5


But, actually, I didn't minus the trivial cases. For example, 'a*c^5'.


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