# Message #4132

From: Eduard Baumann <ed.baumann@bluewin.ch>

Subject: Re: [MC4D] Re: 2x2x2x2: List of useful algorithms (please add yours)

Date: Fri, 14 Sep 2018 15:31:34 +0200

Hi all,

When I do the marvelous 10-move sequence

R [ U2 ] == Iy2 Rz Uy2 Iy2 Lz Ix2 Uy2 Rz Ix2 Dy2

following my picture

the Down half of the right cube ist turned by 180°

Hence R [ D2 ].

Why?

Kind regards

Ed

—– Original Message —–

From: Marc Ringuette ringuette@solarmirror.com [4D_Cubing]

To: 4D_Cubing@yahoogroups.com

Sent: Friday, September 14, 2018 5:29 AM

Subject: Re: [MC4D] Re: 2x2x2x2: List of useful algorithms (please add yours)

Hi Lucas, good job finding your own way through! As you suspected, though, your method is far more complicated than necessary. Using gyros, indeed. :-b

Andy is great with these little sequences, and his method can do exactly what you want using canonical moves. Andy left it as an exercise for the reader, but I’ll take on that exercise! In the RKT style, I think I’d adapt it like this (using the notation R [ R2 ] to represent your

```
( R2 F2 R2 U )2<br>
R [ R2 ] == ( Ox2 Ry' Ox2 Ry Ox2 Rz Ox Rz' )2 Ox2 and cancelling the first and last Ox2 leaves the 15 move alg
R [ R2 ] == Ry' Ox2 Ry Ox2 Rz Ox Rz' Ox2 Ry' Ox2 Ry Ox2 Rz Ox Rz'
```

I think I’ll make sure to keep Andy’s nicely understandable method tucked away as my go-to solution to this issue.

However, we can go 5 moves better!

Just yesterday I finished creating a valid definition of the 2x2x2x2 puzzle encoded into the optimal algorithm finder Ksolve+. The one good algorithm I’ve found so far is for a version of exactly this situation, and it turns out that 10 moves is optimal for the case I had plugged in.

```
R [ U2 ] == Iy2 Rz Uy2 Iy2 Lz Ix2 Uy2 Rz Ix2 Dy2
```

Whoa!

Cheers

Marc

On 9/13/2018 6:26 PM, Andrew Farkas ajfarkas12@gmail.com [4D_Cubing] wrote:

```
<br>
Hello, Lucas! I've been using an RTK-adapted equivalent of (R2 F2 R2 U)2, an 8-move algorithm that can resolve a 180-degree twist; no gyros necessary!
```

On Thu, Sep 13, 2018 at 9:15 PM lucas.denhof.58@gmail.com [4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:

```
<br>
Hey there, I am the ninth solver of the physical 2x2x2x2 and have just joined this group. I wanted to show a new algorithm that I found that does a 180˚ twist on just one of the cubes. I think it will be quite useful but probably also can be very much shortened.
Counting the gyro move as 0 and counting turns it is 39 moves long. I have a video about it here: https://youtu.be/ru_OgVwlfKE
```