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 Post subject: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Wed Sep 19, 2012 9:36 pm

Joined: Fri Aug 31, 2012 6:34 pm
I bought one of these because it looked so cool, and it turns really nicely. Very smooth. But once its scrambled, its mindblowingly hard, for me at least. Considerably beyond my skill set. However no one has posted any tutorials, or even a solve video, for this new puzzle, at least none I've been able to find. Anyone care to light up the darkness for us dullards and share a bit of help solving this amazing puzzle?

Here's a link to this cube on lightake:
http://lightake.com/detail.do/sku.4x4x4 ... hite-44628

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Sep 20, 2012 11:34 am

Joined: Thu Dec 15, 2011 10:04 pm
I saw that puzzle and was intrigued. It seemed that it might be challenging, but I couldn't gauge how much. I made a temporary one out of a 4x4 cube using painters tape:
Attachment:

4x4_Bandaged-1.png [ 254.73 KiB | Viewed 10647 times ]

I will say it is not an easy puzzle! I tried a variety of algorithms and made some headway, but I will have to think about an overall strategy. I put all the unfused blocks on one side of the puzzle using 2x2 cube techniques. This frees the two 4x4 layers to turn:

Attachment:

4x4_Bandaged-2.png [ 202.74 KiB | Viewed 10647 times ]

I then experimented with corner rotations to position different pieces in the two layers. With this method, it is possible to line up pieces and even assemble entire 4x4 faces. The issue is how to preserve these completed sections while working on others. I would like to think that there is a simple strategy that can be applied using basic algorithms, but the lack of working room makes me wonder if this is going to be a case of lengthy commutators.

Attachment:

4x4_Bandaged_Comp1_sm.png [ 123.72 KiB | Viewed 10647 times ]

I have a few more ideas, so I will keep working on it and I look forward to seeing the solutions and ideas of other puzzlers.

_________________

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Sep 20, 2012 6:44 pm

Joined: Fri Aug 31, 2012 6:34 pm
That's certainly a quick and easy way that anyone can sort of model one of these ai 4x4 cubes! The amount of restriction on movement, from the bandaging on this cube, is immense. So, I've started to wonder whether the only way to solve it might be long, counterintuitive algorithms. As you say, there's just not much "working space." Thanks for taking an interest in my post! If you learn more as you go, please share it with us all!

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Sep 20, 2012 8:21 pm

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Hi Pete & prof_grizzlebizzle,

I have this puzzle, it's quite a fun puzzle, you're on the right track Pete.. you just reduce it to a 222. When you make the 222LL like you have, you use 222 LL permutation & orientation algs combined with U twists to reduce the 222 corners.

Don't forget, you can orientate one of the top corners with one of the bottom corners.

Cheers,
Burgo.

_________________
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: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Sep 20, 2012 8:47 pm

Joined: Thu Dec 15, 2011 10:04 pm
Burgo wrote:
Don't forget, you can orientate one of the top corners with one of the bottom corners.

Thanks Burgo, it's encouraging to know I'm on the right track. I've been using corner rotation to position the pieces in different layers.. and I won't soon forget the beginners corner rotation algorithm! I also worked out a clean way to join a completed top and bottom half without messing up other completed sections. I got three of the 4x4 "corners" solved and I am saving the last one for when I'm fresh as it seems it will require temporarily disassembling a completed one.

This is a fun puzzle! Thanks to prof_grizzlebizzle for motivating me to try it. It makes a nice segue from my recent fused cube exploration.

prof_grizzlebizzle wrote:
So, I've started to wonder whether the only way to solve it might be long, counterintuitive algorithms. As you say, there's just not much "working space." Thanks for taking an interest in my post! If you learn more as you go, please share it with us all!
It seems like it should be possible to finish it with just the simple corner rotation/U moves. More tomorrow. This is high interest for me as I just did a video tutorial on the fused cube. Here I thought the fused cube was restricted!

_________________

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Fri Sep 21, 2012 12:57 am

Joined: Mon Feb 28, 2011 4:54 am
Alright, I've wasted enough of today on this already. I couldn't help myself (holidays are no good for this sort of thing...)

I first somehow got 2 complete corner blocks.
Attachment:

shot1.jpg [ 32.26 KiB | Viewed 10552 times ]

Attachment:

shot2.jpg [ 33.21 KiB | Viewed 10552 times ]

Then I went ahead and solved it as much as I could, but I've run out of ideas for the last bit.

Attachment:

shot3.jpg [ 41.06 KiB | Viewed 10552 times ]

Attachment:

shot4.jpg [ 39.93 KiB | Viewed 10552 times ]

Burgo's hints were (as they often deliberately are ) cryptic. It'd also be nice if he didn't write things like
Quote:
you just reduce it to a 222
so nonchalantly. At least pretend it caused you problems.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Fri Sep 21, 2012 1:41 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
I don't mean to be cryptic, I'm not at home and don't have the cube with me. I only solved it once and it was only in one sitting so I don't remember a lot. I didn't hone a method or anything. I remember I cycled the 444centres - `same to same` colour to finish it off (now, I didn't want to say that before: because that does sound cryptic, but if you've played with it you might understand what I mean). Seeing as quite a few are having trouble with it, I'll sit down later and map out a method. I do sit down intuitively and solve some cubes and this was one of those. The solve reminds me of another cube that I've had for quite a while, but it's only just been released (the C4U336):

 Attachments: C4U336.jpg [ 495.28 KiB | Viewed 10548 times ]

_________________
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: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Fri Sep 21, 2012 8:01 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
I just gave it another solve.

Please consider the following sequences as applied to the cube with the 444 cubies all in the Uu layers and the large blocks in the Dd layers.

You can orientate a 222 corner in the U layer with just (RF'R'F)X2 (what happens in Dd is irrelevant).
You can reduce 2 of the 222 corners by just orientating and U turns.

The end game of the remaining 2 222 corners can be solved with U2 twists and this sequence:
(Rr2 Uu Rr2 Uu' Rr2) y' (Rr2 Uu' Rr2 Uu Rr2)
U2
(Rr2 Uu Rr2 Uu' Rr2) y' (Rr2 Uu' Rr2 Uu Rr2)
U
And reorientations of the 222 corners.

Cheers,
Burgo.

_________________
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: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Fri Sep 21, 2012 10:15 pm

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Hi friends,

I made a few photos of the end game. I really think that writing out sequences for this puzzle is innappropriate. The reason is because the sequences will change according to the colours you are trying to match. I have made a photo of the end game, in the hope that it will shed some light on what I am doing. Remember that the 224 componants can be solved with the sequence I put above ^^. I have also included a photo of an interesting situation and a pattern.

 Attachments: bandaged 444 reduction (end game).jpg [ 962.13 KiB | Viewed 10489 times ] bandaged 444 unusual situation.jpg [ 1.42 MiB | Viewed 10489 times ] bandaged 444 pattern.jpg [ 612.85 KiB | Viewed 10489 times ]

_________________
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: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Mon Sep 24, 2012 3:08 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
I made a quick video of a demonstration solve. It isnâ€™t meant to be a comprehensive method video, rather, itâ€™s just to demonstrate what Iâ€™m doing to give you the general idea. I was just going to make it private with a link here, but I decided to make it public. I just hope people on youtube donâ€™t get upset because itâ€™s geared to an advanced TP audience.

http://youtu.be/4UwHCsb6bSM

Cheers,
Burgo.

_________________
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: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Mon Sep 24, 2012 7:04 am

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi friends,

Burgo:
Burgo wrote:
(Rr2 Uu Rr2 Uu' Rr2) y' (Rr2 Uu' Rr2 Uu Rr2)
U2
(Rr2 Uu Rr2 Uu' Rr2) y' (Rr2 Uu' Rr2 Uu Rr2)
U

interesting sequence, very nice.

I tried sequences with 4x4 cube and tape. But I didn't find sequences that only permute a little number of pieces. After some tries my cube was scrambled. Now I use the simulator to find sequences.

Perhaps this puzzle is harder than Burr Cube , is it ?

Cheers,
Andrea

(edit)
I used a similar sequence on many cuboids:
(Rr)2 (Uu) (Rr)2 (Uu)' (Rr)2 (Ff)2 (Uu)' (Ff)2 (Dd) (Rr)2 (Dd)'
It' the same. I saw it, if I looked twice. Because my English is not good I must watch the video more times. I didn't exactly understand , what you do.

Last edited by Andrea on Mon Sep 24, 2012 9:53 am, edited 1 time in total.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Mon Sep 24, 2012 7:21 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Hi Andrea,

I don't think it's harder than the Burr Cube, I think it depends on your approach. For example: reducing the 444 edges and 444 corners (ignoring 444 centres) is very easy.. and then permuting the 444 centres with commutative 3cycles would be possible but very lengthy. I think this would be a reasonable approach though. But for me, I found reducing it more intuitive, although it did take me a while to figure out how to express it. I think if you search for permutation sequences on the simulator you might end up with a less intuitive method on the actual puzzle. Have fun, it's a nice puzzle .

Cheers,
Burgo.

_________________
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: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Mon Sep 24, 2012 9:26 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
I haven't got the AI cube, but I just realized that solving this cube is closely related to my own method of solving the 4x4 Trajber's Octahedron (I do that puzzle face-by-face). Perhaps I'll have to get one now.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Mon Sep 24, 2012 4:11 pm

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi together,
I solved my ugly taped Ai 4x4x4. Perhaps it was an accident. In last steps I got a 3 cycle of center pieces in the last 2x2x2 sub cube. I solved this with combinations with Burgo's and my sequence to swap 2 2x1 blocks and turn with ( (Rr)(Uu)(Rr)'(Uu)' )x2. I needed much time for it.
This is a nice puzzle, I ordered it. Aesthetic is important !
The problem is, to know a system, to turn and exchange the blocks. It's not easy..
Thanks on all writer here.

Cheers,
Andrea

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Tue Sep 25, 2012 3:58 am

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi friends,

One sequence is enough.
The reason is, that permute 2 pieces is equivalent to a 3 cycle + 90 degrees turn.

Exchange the 2 upper front horizontal 2x2x1 cubes
do:

U2 Rr2 Uu Rr2 Uu' Rr2 Ff2 Uu' Ff2 Dd Rr2 U'

To Burgo's way with the y' cuberotation:

Exchanging two 2x2x1 blocks:

U2 Rr2 Uu Rr2 Uu' Rr2 y' Rr2 Uu' Rr2 Uu Rr2 U'

It's a little bit shorter (half)

Cheers,
Andrea

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Wed Sep 26, 2012 7:42 pm

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Hi Andrea,

Thanks for the shorter sequences. I didnâ€™t even think about it, probably because itâ€™s such a small part of the solve. I borrowed that sequence from how I remembered solving the C4Uoffset336. I will put a highlight spoiler with all of my sequences for that puzzle so you can see why I used it. Please donâ€™t read it if you donâ€™t want to know my method for the C4Uoffset336 yet:

[ I used a layer by layer method, so therefore conserving the u layer was important. I solved the first layer with domino algos and then adapted them for the second layer:

/= R2 (square 1 & domino notation)
(A)= (/ Uu / Uuâ€™ /) Uuâ€™Dd (/ Uuâ€™ / Uu /)
(B)= (/ Uu2 / Uu2 /)
(C)= (/ Uu)x2 (/ Uu2)x2 (/ Uu / Uuâ€™ /)

Solving LL corners:
Opposite Swap [BL<>FR]= (A) U2 (A) U
Adjacent Swap [BL<>BR]= U2 (A) U (A)

Solving LL edges:
Opposite 2+2 Swap [F<>B + R<>L]= (B) U (B) Uâ€™
Adjacent 2+2 Swap [F<>R + L<>B]= [(C) U2]x2
3 cycle [R>F>B] (C) U (C) Uâ€™ mirror left handed.

I see now that a reduction method would be more efficient for the C4Uoffset336 too. Iâ€™m not sure which I will prefer, a shorter method or a neater method.. too many choices!
]

Thanks for your contribution, you force me to rethink things .
Cheers,
Burgo.

_________________
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: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Wed Sep 26, 2012 9:38 pm

Joined: Thu Dec 15, 2011 10:04 pm
Is it possible to cleanly swap the two misplaced centres?
Attachment:

Fuse_4x4_Comp_sm.png [ 123.07 KiB | Viewed 10147 times ]

_________________

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Sep 27, 2012 1:56 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Hi Pete,
You need a 3cycle. That's pretty much what I was trying to get across in my video. You have to trade out with another 444centre with a matching colour (Red > Red > Orange, for example). Just try to keep a colour match across the top pairs that become mismatched, like I pointed out.. so that they orientate neatly in the end.

_________________
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: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Sep 27, 2012 8:04 am

Joined: Thu Dec 15, 2011 10:04 pm
Thanks Burgo, in the light of day a 3-cycle with two of the same colour is what it would be. Thanks for the video, I should have been following this thread more carefully .

_________________

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Sat Sep 29, 2012 3:03 pm

Joined: Fri Aug 31, 2012 6:34 pm
Brand new on youtube, but no Part 2 yet.... I've reduced the first two 2x2x2 corners at this point, but I'm still trying to understand the method for the last two.

Thanks to all who have contributed to the discussion!

Brian

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Sat Sep 29, 2012 4:13 pm

Joined: Mon Jun 18, 2012 10:56 am
Location: The Netherlands
Part 2:

Just finished watching, mouth open in amazement

_________________
2x2 PB 04.27 - AO5 08.41 - AO12 09.92 || 4x4 PB 01:57.08 - AO5 02:13.55 - AO12 02:28.19
3x3 PB 20.29 - AO5 28.29 - AO12 29.85 || 5x5 PB 06:13.37 - AO5 07:14.92 || 6x6 PB 17:10.40

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Mon Oct 01, 2012 11:26 am

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi friends,
my first solve was an accident, I think.

I cannot solve this:
Attachment:

Ai444.png [ 479.38 KiB | Viewed 9799 times ]

The red and blue centers are swapped.

Cheers,
Andrea

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Mon Oct 01, 2012 5:07 pm

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Hi Andrea,

That's the same situation for my last 222 corner in the example in my video above ^^. Hope that can help .

Cheers,
Burgo.

_________________
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: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Tue Oct 02, 2012 4:00 am

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Here is a 3-cycle of centres in a structured step by step method.
I'm still waiting for my AI cube, so I have stickered one myself to show my sequence.
(Be warned: This is a bit tedious and visually gifted persons like Burgo will probably lough at me. Maybe, there are some others who can benefit from these details. )

I have made a photo sequence and in each of the 8 situations I'm showing the frontview and backview in Gelatinbrain fashion.
I do not care if the Dd layer of bandaged 222 will change.
I shall use WCA notation and write moves like R2 r2 using the shortcut Rr2 (Rw2 would be a synonym in WCA) as others have done it in this thread.
I shall use Andrea's sequence for swapping two 2x2x1 blocks between the UFL and UFR 222 subcubes.
I'll write [Andrea] for U2 Rr2 Uu Rr2 Uu' Rr2 y' Rr2 Uu' Rr2 Dd y Rr2 U'.

In 1. I have a situation where everything is reduced, just a "pure" 3-cycle of centres is needed.
The arrows in 1. show how the three centre cubies shall move around.

u y' (Ff' Rr Ff Rr')x2 u (Rr Ff' Rr' Ff)x2 y
and get to situation 2.
Now I do [Andrea] and get 3.
I have now permuted several cubies in the 222 blocks originally located at UFL and UFR.
I bring them back by a 3-cycle of 222 blocks in the Uu layer : Ff2 (Uu' Ll2 Uu Rr2)x2 Ff2 and reach situation 4.
The arrows in 4. show what has happened so far.
We recognize that in the 222 block at UFR a single centre at Fur was swapped with the one originally at Ful.
In the 222 block at UFL a lot more has happened shown by the arrows.
If I repeat the whole procedure from the very beginning the Uu layer â€“ all four 222 blocks â€“ will look unchanged.
The whole sequence is self inverse in respect of the Uu layer!

In 5. I have rotated the 222 block UFR counterclockwise by (Ff' Rr Ff Rr')x2.

You can click onto the image to enlarge it!

Now I do the whole lengthy procedure again, the 222 block UFL will be almost unchanged at the end, just the centre Ful will be swapped with the red one located at Fur in 5.

I show two intermediate steps in situations 6. and 7.

At the end I rotate the 222 block at UFR clockwise back to show that the Uu layer in situation 8. looks completely identical to 1. except the 3 centres are now in place.

_________________

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Mon Oct 08, 2012 4:37 pm

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Thank you Konrad for your excellent work. I must study this many times. To solve my new Ai Cube.
After I had this situation and some sequences the situation changes to swapped centers to different 2x2x2 sub cubes. Perhaps there is a scheme to make the strategy easier.

Cheers,
Andrea

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Tue Oct 09, 2012 3:27 am

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Hallo Andrea,
I'll write in German and translate below for others who may be interested.

Es kann gut sein, dass ein viel einfacheres Schema existiert, aber ich bin noch nicht drauf gekommen. Mir fĂ¤llt das Denken in 3-Cycles leichter als anderes. Und mit 2-2 Swaps lĂ¤sst sich leicht ein 3-Cycle machen.
Im Bild 4. sieht man wohl am besten die Idee: Im 222 Block UFL sind intern jeweils zwei Edges und zwei Centres geswappt. Bei einer Wiederholung der gesamten Zugfolge werden diese rĂĽckgĂ¤ngig gemacht.
Weiter ist das Centre Ful mit dem Centre Fur geswappt worden.

Der 222 Block UFR ist in 4. nur in einer Position verĂ¤ndert, nĂ¤mlich durch den Swap Ful <-> Fur.
Also kĂ¶nnen wir einen lĂ¤nglichen Commutator produzieren: X Y X' Y'
X ist die gesamte Prozedur vor 4., Y die Rotation von UFR (Ff' Rr Ff Rr')x2

Wie in 5. zu sehen ist, rotiere ich also den UFR Block und wiederhole die gesamte Zugfolge vor 4. Ich erhalte einen 3-Cycle, an dem ein Centre aus dem Block UFL und zwei aus dem Block UFR teilnehmen.

Es ist weiter zu beobachten, dass jedes Paar der unbandaged 222 BlĂ¶cke eine gemeinsame Farbe haben.
Damit lassen sich dann leicht scheinbare Swaps von zwei Centres machen.

English text:

It may very well be that an easier scheme exists, but I have not found it yet. For me, thinking in 3-cycles is easier than other things. And by using 2-2 swaps we can produce 3-cycles.
You can recognize my idea best by looking at picture 4. In the 222 block UFL two edges and two centres have been swapped internally. After a repetition of the whole move sequence these edges and centres will return to their original location.
Additionally, the centre Ful is swapped with Fur.

The 222 Block UFR has changed one cubie only, the centre Fur by the swap Ful <-> Fur.
We can build a lengthy commutator X Y X' Y'
X is the complete procedure before 4., Y the rotation of block UFR (Ff' Rr Ff Rr')x2.

As you can see in 5. I rotate the UFR block and repeat the complete sequence before 4. I get a pure 3-cycle between one centre cubie in UFL and two in UFR.

You can recognize further that any pair of two un-bandaged 222 blocks share one common colour.
This allows to construct "seeming" swaps of two centres.

_________________

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Tue Oct 09, 2012 11:21 am

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi Burgo,
Quote:
That's the same situation for my last 222 corner in the example in my video above ^^. Hope that can help

Yes. I prefer reducing methods. For me it's easier than difficult 3 cycles of center pieces.

Cheers,
Andrea

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Tue Oct 09, 2012 11:40 am

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany

Thanks for the translation.
The problem is that my sequence swaps two 2x2x1 blocks and changes the position of 2x2x2 blocks, too.
It's difficult for me, to follow the single steps of permutation. Perhaps it's easier for me, to make an orientation on equal colors and 2x1x1 blocks. (Burgo's Video ?) There must exist a system behind this permutations. I must watch to the video from SuperAntoniovivaldi.

Cheers,
Andrea

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Tue Oct 09, 2012 1:48 pm

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi AI Cubers,

Three 2x2x2 are not a problem. The last 2x2x2 cube is the problem.

Example:
Attachment:

ai.jpg [ 90.86 KiB | Viewed 9144 times ]

How to solve it ?

Cheers,
Andrea

(edit)
Trying to solve it, I got the other situations.
There are two main end-situations, I think.
Two centers in different 2x2x2 subcubes are swapped.
Two centers in one 2x2x2 subcube is swapped.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Tue Oct 09, 2012 5:19 pm

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Andrea wrote:
...Trying to solve it, I got the other situations.
There are two main end-situations, I think.
Two centers in different 2x2x2 subcubes are swapped.
Two centers in one 2x2x2 subcube is swapped.
Hi Andrea,
whenever you believe that two centres need to be swapped, you need a 3-cycle involving two centres of an identical colour. (On an ordinary 4x4x4 Supercube you cannot swap just two centres. You can permute them by 3-cycles only.)
Any pair of 222 blocks share one identical colour.

In the situation of your picture above you can group the corner and the three edges of your UFL 222 block and take care of the centres afterwards.

_________________

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Tue Oct 09, 2012 5:47 pm

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Quote:
(On an ordinary 4x4x4 Supercube you cannot swap just two centres.

Yes, I know that. The permutations number is even. But it's possible that 2 edges are swapped.

I watched Burgo's and SuperAntonivivaldi's videos. With many tries I solved my AI Cube.
Each permutation can replaced with blockbuilding.
In my opinion Burgo's and SuperAntonivivaldi's techniques to move blocks is genial. In same cases I got two 2x1x1 swapped blocks they are mirrored. Burgo's idea to build blocks ( he said dead lock) with a different 2x2x2 subcube solved this problem I think. This way is more intuitive. I prefer this. But it's difficult , too.

I wish more postings to work out a reproducible solution. This cube is harder than the Burr/Wall Cube, I think.

Yes, to swap 2 visual exchanged centers needs a 3 cycle. The blockbuilding solve this problem implicit.
Thanks to all writers here.

Cheers,
Andrea

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Wed Oct 17, 2012 3:25 pm

Joined: Fri May 06, 2005 10:13 am
Location: Norway
Here is what i found for making pure 3.cycles on the ai 4x4 bandaged cube:

(assuming all the small cubies are already on the top 2 layers)

1. Edge 3-cycle:
([TR- TD TR TF TD TF-,NU])5 - 70 turns

2. Center 3-cycle:
[[TR- TD TR TF TD TF-,NU] NU- [TR- TD TR TF TD TF-,NU] NU2,TF- TD TF TL TD TL-] - 72 turns

I hope this commutator notation is familiar

Per

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"Life is what happens to you while you are busy making other plans" -John Lennon, Beautiful Boy

Last edited by perfredlund on Wed Oct 17, 2012 4:05 pm, edited 1 time in total.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Wed Oct 17, 2012 4:00 pm

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
perfredlund wrote:
....I hope this commutator notation is familiar

Per
Obviously, you are not a fan of standards

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Wed Oct 17, 2012 4:09 pm

Joined: Fri May 06, 2005 10:13 am
Location: Norway
perfredlund wrote:
....I hope this commutator notation is familiar

Per
Obviously, you are not a fan of standards

The notation is standard (apparently not for those not doing patterns much). And as you can see it is accepted by the applets. The notation used elsewhere in this thread is not supported

Per

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"Life is what happens to you while you are busy making other plans" -John Lennon, Beautiful Boy

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Oct 18, 2012 5:50 am

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
perfredlund wrote:
...The notation is standard (apparently not for those not doing patterns much). And as you can see it is accepted by the applets. The notation used elsewhere in this thread is not supported

Per
Which standard committee? WCA is at least a widely accepted standard. SIGN is another side standard accepted by others. The Randelshofer Standard is new to me.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Oct 18, 2012 11:23 am

Joined: Fri May 06, 2005 10:13 am
Location: Norway
perfredlund wrote:
...The notation is standard (apparently not for those not doing patterns much). And as you can see it is accepted by the applets. The notation used elsewhere in this thread is not supported

Per
Which standard committee? WCA is at least a widely accepted standard. SIGN is another side standard accepted by others. The Randelshofer Standard is new to me.

Haha. It is standard in the sense that many people use it. But probably not by many speedcubers or general puzzle solvers. The whole point of that notation was to include the Java applets so people could see them in action, in a better way than a youtube video could do.

I will work out other basic sequences, like corner 3-cycle and others - but i fear they will be even more taxing to derive ....

Per

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"Life is what happens to you while you are busy making other plans" -John Lennon, Beautiful Boy

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Oct 18, 2012 1:19 pm

Joined: Fri May 06, 2005 10:13 am
Location: Norway
And a nice pattern on this puzzle. Again assuming all the small cubies are in the top 2 layers:

UFR -ring. (169 btm).

Now, that was quite taxing and i'm sure something much better could be found

Per

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"Life is what happens to you while you are busy making other plans" -John Lennon, Beautiful Boy

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Oct 18, 2012 2:49 pm

Joined: Fri May 06, 2005 10:13 am
Location: Norway
One final crazy sequence for tonight:

Corner 2 twist (352 btm).

Per

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"Life is what happens to you while you are busy making other plans" -John Lennon, Beautiful Boy

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Fri Oct 19, 2012 3:00 pm

Joined: Fri May 06, 2005 10:13 am
Location: Norway
Shorter edge 3-cycle (36 btm).

Shorter center 3-cycle (68 btm).

Look at the side permutations to see that it is really a 3-cycle. Center 2-cycle is impossible anyway

Per

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"Life is what happens to you while you are busy making other plans" -John Lennon, Beautiful Boy

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Fri Oct 19, 2012 8:51 pm

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
I have some details to add to my AI444 method to remove some of the mystery:

I will list some priorities:
1. Make 3 full 222 blocks first.
2. Do the minimum of tasks at once.
3. Prioritize the completion of the u layer224 blocks
4. Maintain edge-corner/centre-edge `fingers` in the U layer 224 blocks.
5. Aim for a colour match on the tips of the fingers.
6. Be aware that 3cycles are happening and pre-locate the coloured faces that will need to be involved.
7. Move from: u layer 224 blocks & U layer fingers > 224 blocks > 222 blocks.

I have included another visual sequence and I will explain each photograph [click on the image to enlarge]:
1. I need to move one of these incorrect pairs to the U layer to make a match.
2. Lining one of them up with the yellow will allow me to do this.
3. I need to reorientate the u layer pair. The colour required for me to reorientate them is yellow.
4. I need to do what is necessary to make a yellow block.
5. Orientate the yellow block correctly.
6. Now I have the ability to match my pair by making an orientation.
7 & 8. This is a full 360* cube view to demonstrate the matching pairs.
9. Join them together.
10. Reorient that 222 block. Now the u layer 224 blocks are complete, I am free to work on the fingers in the U layer.

I hope this helps,
Cheers,
Burgo.

 Attachments: File comment: AI444 Sequence 2 AI sequence 2.jpg [ 3.27 MiB | Viewed 8235 times ]

_________________
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: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Sat Oct 20, 2012 8:25 am

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi Burgo,

thank you for this pictures and description. I tried to understand this. I guess the 'fingers' means a 2x1x1 block, is it ?
My solution is similar, I think. Did you watch the video from SuperAntoniovivaldi?

Your pattern pictures above are pretty. Do you made this pattern with this technique ?

To prove that all possible positions are solvable, is difficult.
There are 36 possible positions for the last 2x2x2 cube. ( I don't separate visual permutations, from real permutations)
It must possible first build three 2x2x2 blocks( no problem for me) and then temporary destroy blocks to rebuild new blocks to solve the whole cube.

Hmm. I had many many solves with this cube. Sometimes it was very easy and sometimes it was very difficult to solve it. ( re scramble and try again)

AI=artifical intelligence
But my solution method depends to random.

Cheers,
Andrea

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Sat Oct 27, 2012 8:21 am

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
Hi guys,

A call for help on this one! I've read the thread and there was a vague whistling noise as the discussions went over my head!

I have managed almost all of it without assistance which is a considerable improvement for me! I can reconstitute 3 of the 2x2s with relative ease but for the life of me cannot manage to do the last one. I end up in 1 of three situations:
1) a harlequin type cube with all 8 cubies forming a quilted pattern
2) a single inner column of 4 cubies and. 2x1 outer upper colum assembled but 2 out
3) most distressing just a single corner cubie oriented wrong.

I watched the vids by SuperAntonivivaldi but whils I understand his plans, I cannot actually carry out what he does and I don't really understand why either!

I really thought I was doing well on this one but am completely lost and don't understand the discussions further up. Any further strategy ideas would be helpful.

Kevin

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Kevin

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Sat Oct 27, 2012 6:17 pm

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Hi Andrea and Kevin,

Yes, the fingers are the 1x1x2 blocks, because they are composed of different piece types I wasn't sure what to call them.

I watched Jon's video, it is a very similar strategy to my own. Watching both his and my videos would be helpful to get an understanding of the reduction process. Along with taking a close look at my pictures and commentary.

I made the pattern by repeating an algorithm that I made up, it was just a bit of fun .

All positions are solvable, perhaps it's difficult to `prove`, but they are. At first, before I began targeting situations accurately, getting a clean solve was more random, but after some experience I can isolate what I need to do in clean steps. I will emphasize:
2. Do the minimum of tasks at once.
3. Prioritize the completion of the u layer224 blocks.

Great work on your progress Kevin! The 3rd block is not visually easy and takes forethought and planning, it's good visual practice for the tasks in the 4th block. If you can do the 3rd, you are capable of the 4th.

I can't understand all of your situations, pictures are better, but basically, I think you're saying that the last block is scrambled and you can't solve it .
The situation of having only the 444 corner twisted is actually just the puzzle teasing you, if you solve the 222 from there you will see that it actually has the most pieces that need moving out of all the final situations.. and therefore you need to carefully target the minimum tasks at once, or you will rescramble the puzzle.

All difficult 4th block situations are based around the 3cycles of centres. Edges and corners are very easy to solve. Try a solve of just edges and corners while ignoring 444centres (on the last 2 blocks) and you will quickly see that they are very easy. The complicating factor is the centres.

If I can help any more, just ask, but maybe put a picture of your situation and I can give you a sequence with explanations.

Cheers,
Burgo.

_________________
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: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Wed Oct 31, 2012 5:51 pm

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
At last!

I have actually solved this monster for the first time!

I used a mixture of algorithms for shifting 2x2x1 blocks which I was given by Konrad (he has spent a huge amount of time creating a rather comprehensive document detailing various sequences that can be used) with Burgo's and Jon's pairing up techniques!

Unfortunately I don't yet know whether it was luck. I'm almost afraid to scramble it again!

Konrad has sent me some more information to try. I'm determined to use his system so that future solves won't be a random event.

_________________
Kevin

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Nov 01, 2012 6:14 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
I've been working on the AI444 Checkers tonight, but I don't seem to be able to get better than this. I was trying to get 3 different colours on each of the 1/2 visible 222 blocks in the photos.. to look more symetrical. I'm pretty sure it's not possible.

 Attachments: AI444 checkers.jpg [ 2.36 MiB | Viewed 6814 times ]

_________________
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: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Nov 01, 2012 6:36 am

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
Burgo wrote:
I've been working on the AI444 Checkers tonight, but I don't seem to be able to get better than this. I was trying to get 3 different colours on each of the 1/2 visible 222 blocks in the photos.. to look more symetrical. I'm pretty sure it's not possible.

Now that's just showing off!!!

Here we are! Some of us struggling to solve this monster at all and your just making whatever pretty patterns you fancy with it!! That shows a true mastery of the cube!

Well, like Andrea earlier on, I think my solution must have been a fluke! I have done it twice in succession and now cannot for the life of me repeat the process! I can still get the first 3 2x2x2 cublets solved but again I cannot seem to get my fingers pointing the right way to allow me to do the final solve again!!! I know all the algorithms needed but the strategy required is making my brain hurt!!

In fact I've been playing so long that my hands hurt too!!

_________________
Kevin

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Nov 01, 2012 8:58 am

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi puzzlers,

I tried some pattern , too.
Attachment:

ai-pattern1.jpg [ 126.65 KiB | Viewed 6791 times ]

Attachment:

ai-pattern2.jpg [ 86.53 KiB | Viewed 6791 times ]

Attachment:

ai-pattern3.jpg [ 81.67 KiB | Viewed 6791 times ]

Attachment:

ai-pattern4.jpg [ 108.23 KiB | Viewed 6791 times ]

Not many moves to generate this patters.
These are combinations of:
(Ff)' (Rr)2 U2 y (Rr)2 Ff y2

In a different notation, some people use it: ( lower case means turn two layers together)

f' r2 U2 y r2 f y2

Cheers,
Andrea

(edit)
Turn the sequence 3 times, then you get the first pattern.

(If you get the first pattern you can add a (4 face) chess board pattern and you get the second)

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Nov 01, 2012 1:29 pm

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
Andrea wrote:
Hi puzzlers,

I tried some pattern , too.

Cheers,
Andrea

Et tu Brute?

_________________
Kevin

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Nov 01, 2012 3:37 pm

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Et tu Brute?

I cannot translate this.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yetPosted: Thu Nov 01, 2012 3:45 pm

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
Andrea wrote:
Et tu Brute?

I cannot translate this.

Latin! From Shakespeare - Julius Caesar
Said by Julius Caesar to Brutus just as Brutus stabbed him in the back!

It's a euphemism - what I meant was "Not you too!!!!" after you had also posted fancy patterns like Burgo when I cannot even solve it!

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Kevin

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