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 Post subject: Crazy 4x4 between I and II? (Idea)
PostPosted: Mon Oct 28, 2013 8:08 pm 
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So now that I have a full set of crazy 4x4 puzzles (Thanks juanan!) and have played with them for a little, an idea sprung up upon inspecting crazy 4x4 I and II.

Is it possible to have a crazy 4x4 (circle in this case?) that is between version I and II?
Something like this:
Attachment:
4x4-I.5.jpg
4x4-I.5.jpg [ 28.21 KiB | Viewed 1541 times ]


The areas of concern are the ones coloured in red and orange. But I assume this could be solved with pillowing the puzzle. I'm not sure if there was a topic of this yet (I know the multi-circle thread, but I'm not sure this in particular has been discussed yet)

Does anyone think it is possible, and if so, what kind of challenge would this bring?

And during the creation of the topic, I had an idea of taking half of version 2 and half of version 3, and combining the parts to have something in between them.

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 Post subject: Re: Crazy 4x4 between I and II? (Idea)
PostPosted: Mon Oct 28, 2013 9:58 pm 
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Why bother; it'll just be a II.


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 Post subject: Re: Crazy 4x4 between I and II? (Idea)
PostPosted: Mon Oct 28, 2013 10:23 pm 
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I don't think it would be. But I can see why you'd say that.

Here is version 2:
Attachment:
4x4-II.jpg
4x4-II.jpg [ 52.57 KiB | Viewed 1509 times ]


There are no pieces on this coloured in red like in the image I made. Sure it would be really similar, but It would have a smaller circle than version 2, and a bigger circle in version 1.

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 Post subject: Re: Crazy 4x4 between I and II? (Idea)
PostPosted: Tue Oct 29, 2013 1:01 am 
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Those little red corners outside the circles are what's left of the 444 centres. They're evidenced on the MF8 444 Circle Cube I.

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 Post subject: Re: Crazy 4x4 between I and II? (Idea)
PostPosted: Tue Oct 29, 2013 1:55 am 
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Burgo wrote:
Those little red corners outside the circles are what's left of the 444 centres. They're evidenced on the MF8 444 Circle Cube I.

Yep and recall that the orange pieces are just the "side view" of the 4x4x4 centers so the orange and red pieces are all just views into the same 4x4x4 centers. This intermediate cut adds nothing.

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 Post subject: Re: Crazy 4x4 between I and II? (Idea)
PostPosted: Tue Oct 29, 2013 2:03 am 
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Crazy56U wrote:
Why bother; it'll just be a II.


Actually, it's exactly a IV. There is a slight difference in IV... the red triangles are like the faces on the I, which is not a supercube, but they just get dragged along like one. So not a real difference... but the solve will be easier because of them.

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 Post subject: Re: Crazy 4x4 between I and II? (Idea)
PostPosted: Tue Oct 29, 2013 2:19 pm 
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Well, my original thought was that it is possible to have a circle that includes pieces of version 1 and 2. Since there would still be come center parts that rotate, like version 1, and some wedges from version 2 (orbitals? I don't know exactly what to call these pieces in orange). I would assume that solving would include mixing strategies of version 1 and 2, since we have to consider the pieces in red, and orange at the same time.

I was more interested if the mechanism becomes too difficult to design without the addition of certain supports or solid shape other than a cube. Like, the pieces would be too thin to even 3D print, and may not be printable unless a pillowed shape is used.

Solving it was an after-thought of thinking about a circle smaller than version 2, but bigger than version 1. I'm not an expert on solving, so I added that as a question. The drawing below is what I was imagining.
Attachment:
444 circle sizes.png
444 circle sizes.png [ 15.05 KiB | Viewed 1403 times ]


So the blue is the size of V2, red is V1, and purple (mix of red and blue) is V1.5. I know the image resolution isn't the best, but if the circle extends out of the 4 main centers, it creates the wedges of V2, but not out enough to eliminate the center pieces that rotate around the circle in V1.

So I'm not sure if the opening post was clear enough, but mechanisms are what I'm aiming for, whether possible or not and what would need to change to make it possible. Solving was added to see if an extra challenge was added last minute.

Sorry if that wasn't clear enough

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 Post subject: Re: Crazy 4x4 between I and II? (Idea)
PostPosted: Tue Oct 29, 2013 3:52 pm 
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NXTgen wrote:
Well, my original thought was that it is possible to have a circle that includes pieces of version 1 and 2. Since there would still be come center parts that rotate, like version 1, and some wedges from version 2 (orbitals? I don't know exactly what to call these pieces in orange). I would assume that solving would include mixing strategies of version 1 and 2, since we have to consider the pieces in red, and orange at the same time.
The pieces in orange are the side view of the red pieces.

The Crazy 4x4x4 II is a superset of the Crazy 4x4x4 I. The orange pieces are just a different view of the red pieces. The orange pieces have the side-effect of making all of the red pieces distinct so the Crazy 4x4x4 II solves like a Super 4x4x4.

If you mix the cut between the I and II versions you haven't added anything that isn't already contained in the Crazy 4x4x4 II.

Put another way:

V1: The X-centers have 1 sticker (the red piece)
V2: The X-centers have 2 stickers (the orange pieces)
V1.5: The X-centers have 3 stickers (one red, two orange)

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 Post subject: Re: Crazy 4x4 between I and II? (Idea)
PostPosted: Tue Oct 29, 2013 7:33 pm 
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Okay, bmenrigh, I wasn't understanding fully. But on the side of creating a mechanism (which I'm about to draw up actually) would it be more difficult making the red pieces stay in? In comparison to V1 and V2, if the mf8 style 4x4 was used (3x3>bandage>2x2>4x4), it would be close to impossible to to have them be held in without magnets or a thin wire right? If that is the case, would that also mean that if the mech wouldn't allow room for that, could something like a modified V-cube mech fix that?

While describing these thoughts (to my mother actually :lol: ) I also noticed that if it *is* possible, would that mean that there is a missing puzzle to this set of crazy 4x4s?

Just a thought, but I don't expect any reason to assume that there is a missing link. But would there be any reason to print this if it isn't particularly missing? I may if I get funds for it, but otherwise I may just leave this idea alone.

And sorry again for not understanding fully what you all were saying, I was curious and never really discussed much about circle puzzles.

**Spoiler for a possible upcoming puzzle**

(Except for the "true circle domino" discussed with Archwolf some time ago, but that needs more work before It can be presented :wink: )

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 Post subject: Re: Crazy 4x4 between I and II? (Idea)
PostPosted: Tue Oct 29, 2013 8:39 pm 
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NXTgen wrote:
And sorry again for not understanding fully what you all were saying, I was curious and never really discussed much about circle puzzles.[/color]

Don't worry about it, when I first saw the Crazy 4x4x4 II I didn't understand what it was either. In fact, it was all of Carl's musing about the Crazy 4x4x4 that got me hooked on this forum and it was this post as well as this post that motivated me to apply for an account. I wanted to thank Carl for figuring this out and enabling me to solve mine. Unfortunately the delay between my application and the approval prevented me from responding without bumping the topic.

I'd forgotten that Carl made an image for the puzzle you describe:
Image

It seems Daqing Bao had your circle radius planned as the Crazy 4x4x4 IV (I don't think this ever came out).

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 Post subject: Re: Crazy 4x4 between I and II? (Idea)
PostPosted: Tue Oct 29, 2013 9:04 pm 
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I see now. As for the original sketch, I think they noticed that it would be really hard to keep that small piece outside the circle to stay put, as I see that it is close to impossible without pillowing, wires, or magnets. And would it infringe any patents if this were to be printed? I'd like to see this one come to life if this was dropped from the drawing board so early.

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