Message #4077

From: Marc Ringuette <>
Subject: 2x2x2x2: List of useful algorithms (please add yours)
Date: Sat, 28 Jul 2018 14:46:22 -0700

Let’s start compiling a list of useful 2x2x2x2 algorithms, both physical
and virtual.   Feel free to provide them either written out, or on
video, or as MC4D macros, and in whatever move set you like.

I suggest that we put a fairly strong emphasis on fewest-moves as a
primary criterion for a good algorithm.

Does anybody have a collection of move-efficient algorithms for the
virtual 2^4 or 3^4 ?

My focus is on generally useful algorithms like 3-cycles.   However,
toward the bottom I have put some important "translation" algorithms for
copying virtual moves on the physical puzzle and vice versa.

More, please!!


2x2x2x2 algorithm list v1.00:

3-cycle:   (16 moves canonical)
       in Marc’s virtual+physical notation:   LF’  (FO2 LO’ FO2 LO FO2)
LF  OR2 LF’  (FO2 LO’ FO2 LO FO2) LF  OR2
       in ROIL xyz notation:   Lz’  (Fz2 Lx Fz2 Lx’ Fz2) Lz  Ox2   Lz’ 
(Fz2 Lx Fz2 Lx’ Fz2) Lz  Ox2

Two 2-cycles:  (34 moves canonical, by commuting the above 3-cycle with
Ry – but I’m sure we can do far better)

Two opposite twists:  (14 moves
physical using ROIL Zero)
       in ROIL Zero notation:  R [ R U R’ U R U2 R’    B U2 B’ U’ B U’ B’ ]
       Translated to 28 moves canonical:  Ox Rz Ox Rz’ Ox’ Rz Ox Rz’ Ox
Rz Ox2 Rz’ Ox’     Ry    Ox Rz Ox2 Rz’ Ox’ Rz Ox’ Rz’ Ox Rz Ox’ Rz’
Ox’    Ry’

Monoflip:  (35 moves
physical using ROIL Zero, 88 moves virtual)

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)

Exchange a twist between L and R subcubes:
   from Andy F:     Iy2   R [ U’ R’ U’ R U2 ]   Iy2   (7 moves physical
using ROIL Zero, preserves neither L nor R fully, use before first OLL)

    Melinda’s gyro (which is a FOro to Marc):
    ROIL FOro:   Iy Oy’ Rx2 Bz2 Uy2 Rx2
    FUro using double long restack:

Physical Iy on virtual:
   Based on this from Michael Gottlieb:      Iy (physical) = IU’ RO2 IF
RO2 IU RO2 IF’ RO2 IU (virtual)

Virtual IU and IF on physical:
    IU (virt) ==  I [ F2 U2 R2 F B ]  (phys) (ROIL Zero, from Michael
    IF (virt)  ==  I [ U2 F2 L2 U D ]  (phys) (ROIL Zero, from Michael