Message #4131

From: Marc Ringuette <ringuette@solarmirror.com>
Subject: Re: [MC4D] Re: 2x2x2x2: List of useful algorithms (please add yours)
Date: Thu, 13 Sep 2018 20:29:10 -0700

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
     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:
> 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
> <mailto:lucas.denhof.58@gmail.com> [4D_Cubing]
> <4D_Cubing@yahoogroups.com <mailto:4D_Cubing@yahoogroups.com>> wrote:
>
> 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
>
>