# Message #4141

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

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

Date: Sun, 16 Sep 2018 18:24:47 +0200

Nothing else than MS-Excel (then screen capture and MS-Paint for trimming).

Best regards

Ed

—– Original Message —–

From: Melinda Green melinda@superliminal.com [4D_Cubing]

To: 4D_Cubing@yahoogroups.com

Sent: Saturday, September 15, 2018 11:02 AM

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

Whoa indeed, Marc! Look at you hoovering the 4th dimension to find algorithmic gems!

Now maybe I’m doing something wrong but when I finish your 10 move sequence it’s still one clamshell move (3 canonical twists) away from R[U2].

Also, Ed: I love your coordinate system diagram! It belongs in the wiki in an entry for this puzzle. What software did you use to make it?

-Melinda

On 9/13/2018 8:29 PM, Marc Ringuette ringuette@solarmirror.com [4D_Cubing] wrote:

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!
```