how to reach single corner twist in physical 2x2x2x2 ?

[Eleanor Abernathy]

Hi all, have enyone found the way to reach the equivalent to 2nd four-color series at phisical 2x2x2x2? I need to reach this

I have the cube like this

How can I get this?

Does anyhone know , or have any video? I don't understand the notation yet :S

[Chetan Vashisht]

From my understanding of the cube, this is possible. But its extremely difficult to achieve in practice. 

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[jonathan nifenecker]

Yes it's doable, I'm pretty sure I have a macro on mc4d for that but it is certainly hundreds of modes given how I builded my macro set... So I Doubt it would be usefull on the physical one. 

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[Eleanor Abernathy]

The fact is that I think I did something strange, maybe not legal during twisting. I've been finally able to solve one pair of faces and when reassembling the rest of the puzzle I got a single 4-pieces layer 90 degree tiwst, I think that's not possible, so.... I hope this won't happen again :S 

I'm working on a tutorial and I dunno if I should include this parity, since I have no idea how to handle it :O

Thank you!

[Marc Ringuette]

I haven't touched any of this in two years, but Eleanor's question is
right in my wheelhouse from back then.

We're calling this case the "monoflip".   Here are two monoflip
algorithms, depending on whether or not you think it is tasteful to pick
up a 2x2x2 subcube and twiddle it separately while observing "0 mod 4"
parity.

If you think half-puzzle moves are okay, as in my ROIL Zero moveset,
here's the video for you (7m 34s).  I give a solution in 35
easy-to-execute Roil Zero moves on the physical puzzle and 88 moves in
the virtual puzzle, solving them side-by-side.

  https://www.youtube.com/watch?v=k6ZSu0xOPbQ

However, the Roil Zero business -- calling it kosher to pick up a
half-puzzle and twiddle it while observing a parity rule in your head --
is not to everyone's tastes, and my mc4d macro equivalence for ROIL Zero
is more complicated than the one for full-puzzle ROIL.   If you prefer
to restrict yourself to full-puzzle moves, Tom Rokicki ran a big
computer for a day to get the optimal answer for ROIL:

    Rx Ry Oy' Lz Oy Ry Iy Rx Iz Rx Rz Iz' Rx' Iy' Ry' Oy' Lz' Oy

I tried the moves on a puzzle just now and it worked.

I'll attach a mc4d macro file that you can use to play with this
solution (see 3:05 in the above video for instructions on my
standardized macro handles, i.e. https://youtu.be/k6ZSu0xOPbQ?t=185 ).  
You might also need to review my playlist on the ROIL moveset, linked
below, so you can see how to perform the algorithm on the physical
puzzle and understand how the equivalency works with the virtual puzzle.

https://www.youtube.com/playlist?list=PLNqYnY8yQrGP2c6lr_63306Pj5gJZa8Rn

I've also got some partially documented stuff at
https://github.com/ringuette/2222 that someone could poke around with;
mostly ksolve+ encodings that I used to search for good algorithms, and
provided to Tom Rokicki to use with his search code.  I played around
with a dozen or so movesets that led to drastically different search
spaces.  Interesting stuff, but I got tired and dropped it.   It may be
worth someone pursuing someday; please pick up the ball and run with it.


Finally, I might mention that you never need to use a full monoflip
algorithm in a normal solve.  When solving a scrambled puzzle using my
own Roil Zero solving method, I used an abbreviated monoflip alg that
only preserves the In and Out faces, modified from a nice little
algorithm from Andy Farkas.  The idea is to spot it as soon as possible
and fix it early.

Monoflip, solving In+Out faces only:   (12 moves physical using ROIL
Zero, 3 cases)
   RUFI by x2:       Rzy  I [ U F U' F U F2 U' ] Iy Lx2 Iy'  Rz'
   RUFI by y2:       Ry'z'  I [ U F U' F U F2 U' ] Iy Lx2 Iy'  Ry
   RUFI by z2:       Rzy  Iy Lx2 Iy'  I [ U F2 U' F' U F' U' ]  Rz'
(those are sideways Sune, Sune, and Antisune, inside the brackets,
executed on the In subcube)


Good luck,
Marc

[Eleanor Abernathy]

Hi Marc

I can't believe I didn't find your video while searching for the algorithm. It's a really good job. I'll study them more in depth.

I almost fully understood what you meant, except for "ROIL" (acronym?) and "Sune" and "Antisune". I'm new in 2x2x2x2 and my English, well, is good but limited :S

Two years ago I'd have taken the ball and continued the project, I'd have been a really interesting final degree thesis for a maths degree (I did one about a quantum algorithm ). I'll think about it :)

Of course I'll give a link to your videos when I upload my solution with tutorial (I think it'll be the first in Spanish) and mention you on my "thanks to" list

Best Regards and happy puzzling

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