The title is a little general, but it should be, as I have a lot to share about forming several types of 2-cycle inner-layer odd permutation algorithms.

To begin, why not start with the "Pure Edge Flip" (my favorite, obviously).

I would first like to show you how to derive common OLL parity algorithms by hand. To do this, I have taken the time to make tutorial videos for three popular algorithms. Each of the three algorithm's derivations are two videos long.

*Note...*

To begin, why not start with the "Pure Edge Flip" (my favorite, obviously).

I would first like to show you how to derive common OLL parity algorithms by hand. To do this, I have taken the time to make tutorial videos for three popular algorithms. Each of the three algorithm's derivations are two videos long.

Methods for Forming 2-Cycle Odd Parity Algorithms for Big Cubes]]>

Melinda Green, one of the authors of the java program Magic Cube 4D, has developed a physical analog of the 2x2x2x2 hypercube puzzle that is quite nice, and we'd like to invite you to help us analyze it.

Here's Melinda's intro video, with some useful links in the description.

There's a link to the MC4D mailing list...

Melinda's physical 2x2x2x2 puzzle]]>

On a 3×3×3 and related puzzles (e.g. big cubes), there is a considerable amount of variety in the types of subgroups generated by face moves. (We will not consider generating sets with move sequences longer than...

Megaminx "half turn subgroups" <U, R2> and <U, R2, F2>]]>

Hey! Any ZZ solvers? Would you mind filling this out? https://goo.gl/forms/1ROTK68T9AFI1Lny2]]>

I study the period of algorithms.

Let A be an algorithm. A is "k-periodic" if A^k (A repetead k times) is the equivalent of doing nothing.

For instance, (RUR'U') is 12-periodic, 36-periodic, and its smallest period is 6.

I'm searching algorithms whose smallest period is 11 and whose height (HTM) is as small as possible.

Currently I found this one (with a program), its height is 10 :

D' L R' F U' R U' D F' L

But maybe...

Wanted: 11-periodic optimal algorithm]]>

I'm in the seek of all the 5 edge commutators (EO preserve preferably) like this one:

R2 F2 R2 U' x 2

(all the cycle shifts are already taken into account)

So if you have any commutator (8 mover or fewer even better) is really well appreaciated.]]>

Then there is all the methods which do corners first (or edges first) like most of the bld methods.

Then there is all of the fmc approaches.

But then there is the question how Roux fits into this...

Thats my view on this. What do you think? How would you group the methods?]]>

It compares algorithm count and move count for several popular Last Slot / Last Layer variants for methods that orient edges beforehand (Petrus, ZZ, Heise, ie good methods). Frequency-normalized...

Comparison of ZZ/Petrus LS/LL Methods]]>

tl;dr: 143 OBTM 141 OBTM 135 OBTM (2017-10-31) 134 OBTM (2018-05-15) 130 OBTM (2018-05-20).

I finished writing a 5x5x5 solver about three weeks ago, and in the time since I've mostly been working on trying to get a "good" upper bound for the 5x5x5 God's number in OBTM. I'm not entirely satisfied with this analysis, because according to...

5x5x5 OBTM upper bound]]>

I know (or...

Positions vs Possible Scrambles]]>

- Orient edges and get them into their slices (18 moves)
- Edges are then placed ( 9 moves)
- Corners are done (36 moves)

Thistlethwaite's 63 move solution]]>

The first phase puts six edges (DF, DR, DB, DL, FL, and BL) into the correct orientation, solves the DLF and DBL corner pieces, and also solves six face pieces (or center...

2-phase Curvy Copter analysis (sans jumbling)]]>

The kilominx has (19!/2) ⋅ 3^18 ~ 24 septillion states (with a fixed corner), which is well beyond what we can exhaustively enumerate. Even with full symmetry+antisymmetry reduction, that's still around 98 sextillion states, which is a lot larger than the number of 3×3×3 states

Kilominx God's number bounds]]>

I'm posting this in the theory section because I don't actually have this puzzle yet and I was a bit curious about its solving process. Essentially, while the shape of the puzzle changes with every...

YJ Floppy Ghost Cube]]>

The steps are as follows:

- Develop a notation which can be used to write down algorithms for your puzzle. You will need a character representation for every twistable part of the puzzle and a character representation for every direction a part can be twisted.

- Decide what order you want...

Generic Solving Method]]>

Pure Flips

There are four essentially different pure 2-flips. If the edges to be flipped are adjacent (as in UF and UR), 6 J-perms are...

J-Perm Metric]]>