# Message #4076

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

Subject: Re: ROIL Zero explanation, was Re: [MC4D] correction and question

Date: Sat, 28 Jul 2018 20:04:26 +0200

Thanks a lot!

Ed

—– Original Message —–

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

To: 4D_Cubing@yahoogroups.com

Sent: Saturday, July 28, 2018 7:15 PM

Subject: ROIL Zero explanation, was Re: [MC4D] correction and question

On 7/28/2018 3:06 AM, ‘Eduard Baumann’ ed.baumann@bluewin.ch [4D_Cubing] wrote:

```
Question to Marc: what is R[U] exactly in the names of the macro's?
```

Hi, Ed! I explain this in my videos, but I should write it down too. Here it is.

In my ROIL Zero macros,

```
R [ U ] == on the R cube, make a U move (leaving a side-effect on the buffer)<br>
== Rz2 Ix' Rz2
```

and similarly for the other R [ DLRFB ] using the same buffer, namely, the four In+Left pieces. This is similar to the historical RKT solving style for MC4D.

If you perform any sequence of R [] such that the sum of the clockwise quarter-twists adds up to 0 mod 4, then the buffer will emerge unchanged. For instance,

```
Sune on R == R [ R U R' U R U2 R' ] == a rearrangement of the U face of the R cube leaving no side-effects elsewhere.
```

These macros allow MC4D to follow along with a physical 2x2x2x2 solution that is done in my convenient ROIL Zero style, that allows the solver to perform 3D algorithms on any of the R, L, I, or O subcubes of the physical puzzle, performing a sequence of (individually parity-violating) 4-cycles, AS LONG AS the sum of the turns adds up to 0 mod 4 when the puzzle halves are reattached.

Nobody but me has used the ROIL Zero style yet, except for "Can Chris Solve", who did something almost identical in his followup video where he reconciles his use of 3D algorithms with the requirements of permutation parity on the MC4D 2^4 puzzle. I’ve cued it up here:

https://youtu.be/S6SYi49VZgU?t=2m50s

A few other solvers have simply ignored permutation parity, as I did a year ago until it was brought to my attention. Ignoring parity – freely using 4-cycle twists without counting parity at all – is even more convenient, and internally consistent, but solves a slightly different puzzle than our gold standard of MC4D. Doing so leads to a situation where the physical puzzle can spend a long time in an odd permutation parity state that cannot be duplicated by MC4D at all. Maybe this is fine for you! I, and Chris, decided to split the difference. We retained our really convenient shorthand for performing 3D algorithms on the physical puzzle, while doing enough housekeeping to ensure that the physical puzzle and MC4D are always in compatible states when the subcubes are reattached at the end of each algorithm. By providing these macros, I’m making our approach as kosher as possible, by providing an explicit way to translate any carefully executed ROIL Zero solution into a canonical one.

Cheers

Marc