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

Thanks for the shorter sequences. I didn’t even think about it, probably because it’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 don’t read it if you don’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 / Uu’ /) Uu’Dd (/ Uu’ / Uu /)
(B)= (/ Uu2 / Uu2 /)
(C)= (/ Uu)x2 (/ Uu2)x2 (/ Uu / Uu’ /)

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) U’
Adjacent 2+2 Swap [F<>R + L<>B]= [(C) U2]x2
3 cycle [R>F>B] (C) U (C) U’ mirror left handed.

I see now that a reduction method would be more efficient for the C4Uoffset336 too. I’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.

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PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Wed Sep 26, 2012 9:38 pm 
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Is it possible to cleanly swap the two misplaced centres?
Attachment:
Fuse_4x4_Comp_sm.png
Fuse_4x4_Comp_sm.png [ 123.07 KiB | Viewed 11038 times ]

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

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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: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Thu Sep 27, 2012 8:04 am 
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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 :shock: .

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

http://www.youtube.com/watch?v=b62HPjlUmYQ&feature=plcp

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 yet
PostPosted: Sat Sep 29, 2012 4:13 pm 
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Part 2:

http://www.youtube.com/watch?v=DQeZ0iDqt4s


Just finished watching, mouth open in amazement :D


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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Mon Oct 01, 2012 11:26 am 
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Hi friends,
my first solve was an accident, I think.

I cannot solve this:
Attachment:
Ai444.png
Ai444.png [ 479.38 KiB | Viewed 10690 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 yet
PostPosted: Mon Oct 01, 2012 5:07 pm 
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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.

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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: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Tue Oct 02, 2012 4:00 am 
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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. :wink: )

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.

I start with
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 – all four 222 blocks – 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!

Image

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 yet
PostPosted: Mon Oct 08, 2012 4:37 pm 
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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 yet
PostPosted: Tue Oct 09, 2012 3:27 am 
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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 fällt das Denken in 3-Cycles leichter als anderes. Und mit 2-2 Swaps lässt 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 rückgängig gemacht.
Weiter ist das Centre Ful mit dem Centre Fur geswappt worden.

Der 222 Block UFR ist in 4. nur in einer Position verändert, nämlich durch den Swap Ful <-> Fur.
Also können wir einen länglichen 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 Blöcke 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 yet
PostPosted: Tue Oct 09, 2012 11:21 am 
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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.
I try to understand your scheme behind your solving. I watched your video more times.

Cheers,
Andrea


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

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 yet
PostPosted: Tue Oct 09, 2012 1:48 pm 
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Hi AI Cubers,

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

Example:
Attachment:
ai.jpg
ai.jpg [ 90.86 KiB | Viewed 10035 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 yet
PostPosted: Tue Oct 09, 2012 5:19 pm 
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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 yet
PostPosted: Tue Oct 09, 2012 5:47 pm 
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Hi Konrad and Burgo,
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.

Konrad:
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 yet
PostPosted: Wed Oct 17, 2012 3:25 pm 
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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 8-)

Per

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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 yet
PostPosted: Wed Oct 17, 2012 4:00 pm 
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perfredlund wrote:
....I hope this commutator notation is familiar 8-)

Per
Obviously, you are not a fan of standards :wink:

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Wed Oct 17, 2012 4:09 pm 
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Konrad wrote:
perfredlund wrote:
....I hope this commutator notation is familiar 8-)

Per
Obviously, you are not a fan of standards :wink:


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 :oops:

Per :solved:

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

Per :solved:
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 yet
PostPosted: Thu Oct 18, 2012 11:23 am 
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Konrad wrote:
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 :oops:

Per :solved:
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. :wink:

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

Per

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Thu Oct 18, 2012 2:49 pm 
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One final crazy sequence for tonight:

Corner 2 twist (352 btm).

Per :scrambled:

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

Per

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Fri Oct 19, 2012 8:51 pm 
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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
AI sequence 2.jpg [ 3.27 MiB | Viewed 9126 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 yet
PostPosted: Sat Oct 20, 2012 8:25 am 
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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. :lol: :oops:

Cheers,
Andrea


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

Kevin

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

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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: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Wed Oct 31, 2012 5:51 pm 
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At last! :D

I have actually solved this monster for the first time! 8-)

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.

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


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AI444 checkers.jpg
AI444 checkers.jpg [ 2.36 MiB | Viewed 7705 times ]

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Thu Nov 01, 2012 6:36 am 
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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!!! :shock: :shock: :shock:

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! 8-)

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!! :cry:

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

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

I tried some pattern , too.
Attachment:
ai-pattern1.jpg
ai-pattern1.jpg [ 126.65 KiB | Viewed 7682 times ]

Attachment:
ai-pattern2.jpg
ai-pattern2.jpg [ 86.53 KiB | Viewed 7682 times ]

Attachment:
ai-pattern3.jpg
ai-pattern3.jpg [ 81.67 KiB | Viewed 7682 times ]

Attachment:
ai-pattern4.jpg
ai-pattern4.jpg [ 108.23 KiB | Viewed 7682 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 yet
PostPosted: Thu Nov 01, 2012 1:29 pm 
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Andrea wrote:
Hi puzzlers,

I tried some pattern , too.

Cheers,
Andrea

Et tu Brute?

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Thu Nov 01, 2012 3:37 pm 
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Puzzlemad wrote:
Et tu Brute?

I cannot translate this.


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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Thu Nov 01, 2012 3:45 pm 
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Andrea wrote:
Puzzlemad 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! :oops:

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Fri Nov 02, 2012 3:32 am 
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Hi Kevin,
Kevin wrote:
1) a harlequin type cube with all 8 cubies forming a quilted pattern

Yes

There are two cases,
1) the corner belong to an edge, or to more edges
2) the corner belongs to no edge, all adjacent colors are wrong

solution of case 2 = transform it to case 1)
case 2)
Bring the corner with a 90 degree turn away. Exchange the 2x2x2 blocks in the way that edge has same color as the 2x2x2 block. This causes minimal destruction of builded blocks.
Then turn the 2x2x2 to left or right. After that you can turn it back and the corner belongs to one edge.
Now you can repair the other blocks.

case 1)

The finger (2x1x1 block) must lie horizontal in the upper layer. Look to the sticker with different color adjacent to the finger. Permute the other 2x2x2 cubes in that way that the color of destination position matches. You can exchange 2x2x1 inner blocks and 2x2x1 outer horizontal blocks and turn this blocks to make a match with the moving "fingers".
If two "fingers" have the same colors on the heads then I name it "candidate". You can move "candidates" to its color and turn this position. In this way you transform your "fingers" to 2x2x1 blocks.

To solve the 2x2x1 blocks, its not a problem, I think.

Perhaps my English is too much poor. I must make a video, I think.

Cheers,
Andrea


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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Fri Nov 02, 2012 4:05 am 
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Better and faster exchanging two 2x2x2 blocks.

I developed this sequence in past ( perhaps 15 years ago). The sequence, like an idea of ultimate solution for big-cubes can exchange corners, edges or groups of edges.
It exchanges the right top corners and the corners in down layer.
The sequence is self-inverse!

sequence= F D' R D2 R' D F'

try it, its very fast !

To make a clean outer 2x2x1 exchange make
U sequence U sequence U
To make a clean inner 2x2x1 exchange make
uU' sequence uU' sequence uU'

(uU' in multislice notation is u in wca notation)

perhaps this makes it a little bit smoother to solve the ai 444.
advantage is, that no cube-rotation is included.

Cheers,
Andrea


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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Sat Nov 03, 2012 12:15 am 
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Hi Andrea,

Thanks for sharing all your sequences. I like your patterns more than mine. I didn't use a sequence to generate them this time, in this case I found it easier just to solve to that state.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Sat Nov 03, 2012 10:06 am 
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I got my AI cube (white :( ) two days ago.
Andrea, thank you for sharing your 2x2x1 swap!

Here is my move sequence for swapping 2x2x1 blocks:
I'll use WCA notation:
e.g. u = inner slice below U; Uw = (U u) (Uw spoken as U wide is a synonym to 2U in WCA as well). The SiGN notation Andrea is referring to is quite different (e.g. 2U is the inner layer below U and u are two layers together). I think it is less confusing if we stick with one standard wthin one thread (instead of three, WCA, Randlshofer, SiGN :wink: ).

I use on almost any cuboids a pure corner 3-cycle:
F2 (R2 U' L2 U)x2 F2 (10 moves) which is the cuboid version of the Corner Piece Series (CPS) R U' L' U R' U' L U.
It can be used on cuboids with edges too achieving a pure corner 3-cycle.

As I want to 3-cycle 2x2x2 blocks, it becomes Fw2 (Rw2 Uw' Lw2 Uw)x2 Fw2.
Now I add two outer layer moves to get a 2x2x1 swap: U2 Fw2 (Rw2 Uw' Lw2 Uw)x2 Fw2 U (12 turns).
This swaps the 2x2x1 blocks originally located at UFL and UFR relative to the u layer blocks.

Image
I use front-view / back-view pictures as in Gelatinbrain.
Situation 1 shows the setup, situation 2 the result of the 12 moves sequence U2 Fw2 (Rw2 Uw' Lw2 Uw)x2 Fw2 U

Andrea's move sequence has the advantage that the reduced blocks remain at their original position.
It is a bit longer, if you do not care about the final location.
My sequence has the advantage that the basic sequence will look familiar to most solvers and it can be used on any cuboids as well.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Sat Nov 03, 2012 5:16 pm 
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My sequence for swapping two 2x2x1 blocks is I think quite similar to Andrea's. It's very intuitive.

Hold the two needing swapping at UFL and UFR.

Starting with these (showing the UFL and UFR needing swapping)
Attachment:
003.JPG
003.JPG [ 45.08 KiB | Viewed 3115 times ]

Attachment:
004.JPG
004.JPG [ 44.6 KiB | Viewed 3115 times ]

and then carrying out

U2 y Ll Dd (Ll)' (Rr)' (Dd)' Rr Ll Dd (Ll)' U' y'

give us

Attachment:
005.JPG
005.JPG [ 31.85 KiB | Viewed 3115 times ]

Attachment:
006.JPG
006.JPG [ 43.07 KiB | Viewed 3115 times ]


I worked this out when I was solving the cubic 336, and realised it'd apply to this as well. Of course, i could leave out the y and y' and alter the corner swap in the middle, but this is what works for me.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Sun Nov 04, 2012 3:41 am 
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Phew!

I have just spent the best part of a week working my way through the AI cube. When I say a week, i mean that my dayjob got in the way, so probably "a number of hours" is more accurate. I take longer than some others around here to "grok" things. And I decided I needed to get my head around it. I've appreciated Burgo's original example video, and i'm also very grateful to him for helping me get my head around the main concept of the colour matching, via PM. That was the thing that was missing from my understanding.

Once I "saw" what needed to be done, it made figuring out the right approach for each 4th block case a lot easier. The hardest one was the twisted corner, but I got there today. I really feel like getting my head around this cube has improved my solving skills, which is strange, since there's only one sequence being used. It's more in the sense of thinking through why to do what when.

As usual, I've made some videos showing the whole process from start to finish, including 6 cases of a 4th block scenario. And as usual, the videos are geared towards those who need things explained (hopefully) simply and clearly. I have no doubt that some of the methods may not be the most efficient, but I think they're ok.

The videos with written tutorial are here.

The individual videos are as follows:
Part 0: Preliminaries
Part 1: Block 1
Part 2: Block 2
Part 3: Block 3
Part 4: Block 4 Example 1 (edge unmatched with its center)
Part 4: Block 4 Example 2 (three edge-center pairs needing to cycle around the corner)
Part 4: Block 4 Example 3 (three centers need to cycle around the corner)
Part 4: Block 4 Example 4 (twisted corner and two swapped centers)
Part 4: Block 4 Example 5 (three edges need to cycle around the corner)
Part 4: Block 4 Example 6 (single twisted corner)
Part 5: Solve Reduced Cube

And finally, could prof_grizzlebizzle consider changing the title of this thread? :lol:

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Last edited by rline on Fri Nov 15, 2013 10:15 pm, edited 2 times in total.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Sun Nov 04, 2012 4:40 am 
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Hi rline,

your video
Quote:
single twisted corner.


Great work. Respect. Good description.


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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Sun Nov 04, 2012 8:42 am 
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Pattern:
4 Zig Zag and 2 checkerboard in checkerboard


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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Sun Nov 04, 2012 8:44 am 
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Hi rline and all other

perhaps this is one of the hardest cases:
Attachment:
harlequin.jpg
harlequin.jpg [ 16.08 KiB | Viewed 3072 times ]


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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Sun Nov 04, 2012 2:34 pm 
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Andrea wrote:
Hi rline and all other

perhaps this is one of the hardest cases:
Attachment:
harlequin.jpg
Hi Andrea,
nice pattern! :)
Thinking in two swaps of edges makes your case pretty easy.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Sun Nov 04, 2012 4:54 pm 
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Andrea wrote:
Hi puzzlers,

I tried some pattern , too.
Attachment:
ai-pattern1.jpg

Attachment:
ai-pattern2.jpg

Attachment:
ai-pattern3.jpg

Attachment:
ai-pattern4.jpg


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)


Here is an applet visualisation of this pattern:

Zig-Zag 4 sides (15 btm).

A bit optimised for good measure 8-)

Per :wink:

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Mon Nov 05, 2012 1:40 pm 
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This has rapidly become one of my current favourite cubes!
It doesn't look like much because of the big blocks but giving a scrambled one to a non-puzzler very rapidly they realise they cannot do anything at all with the small cubies!

Initial help from Konrad (via PM) has allowed me to solve it with some considerable effort! That man is a genius!!! I just do not know how he does it!! A 9 page pdf file of helpful hints, beautifully formatted with pictures! This provided me with some much needed techniques!

Then, Rline adds in his website instructions and I can combine the 2! I can now solve this cube from any position! I now don't even need to refer to notes for algorithms!!
Thanks very very much guys!! :D :D :D

Twisty Puzzles is an awesome resource, the boards and the people! I have sent several of my blog corespondents here to whet their appetites for twisty puzzles or get detailed information!! 8-)

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Mon Nov 05, 2012 1:55 pm 
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Hi. I'm trying to avoid using other people's algorithms or solution videos for this one, so I'm really just looking for a hint. I can get 3 complete 2x2x2 blocks easily enough. The only thing useful I've found beyond this is an intuitive way to swap the top 2x2x1 section of two opposite 2x2x2 blocks. I'm wondering if this alone is sufficient to solve or if I should start looking for some other sequences.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Mon Nov 05, 2012 2:56 pm 
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themathkid wrote:
Hi. I'm trying to avoid using other people's algorithms or solution videos for this one, so I'm really just looking for a hint. I can get 3 complete 2x2x2 blocks easily enough. The only thing useful I've found beyond this is an intuitive way to swap the top 2x2x1 section of two opposite 2x2x2 blocks. I'm wondering if this alone is sufficient to solve or if I should start looking for some other sequences.

You'll need a little more than just that unfortunately. What you need to be able to do is make the 2x1x1 fingers from the disparate pieces everywhere. Generally, you want to colour match edges with centers from a different block. Sometimes the corner is twisted so you need to make sure that ends up colour matching correctly with an edge as well. I don't think anyone could post sequences here for reducing it (Konrad has some sequences for 3-cycles above I think) because the turns you need to do depend on the colours you're trying to match. But for reducing it first to the 2x1x1 fingers, and then to the 2x2x1 blocks, you're generally trying to match colour without breaking much of what you've done already. (The only sequences you need are things like (F'RFR')x2 and variations, along with U turns.)

I'm aware this is still vague, but you only wanted hints. As you know, there are now a number of videos to look at if you need to.

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 Post subject: Re: Cubetwist ai 4x4 bandaged cube -- no solution videos yet
PostPosted: Mon Nov 05, 2012 4:34 pm 
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Thanks. I kind of understand what you're saying. I'll keep working on it. I really like this puzzle and want to try to solve it on my own, but it's wearing me down.

UPDATE: I managed to finally solve it! I don't know if it was luck or not. I decided the key was to break a third 2x2x2 block [I had previously tried to keep two 2x2x2 blocks together all the time]. The first time I tried it, it worked! This is possibly the most complicated puzzle I have solved! Yay!

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