Positions vs Possible Scrambles]]>

Scramble:

R' U' L R B R' L' B' U B U' l' r'

x' y' w x z x' w' z' y z y' W' X'

[R']

r R Dw R [U'] R' Dw B [ U ] r

rx'

X x ·Y x ry' x' ·Y z ry X

Layers/slices:

Rotation on x-axis (X, 2X, 3X, 4X and so on; ·X, ·2X, ·3X, ·4X and so on)

Rotation on y-axis (Y, 2Y, 3Y, 4Y and so on; ·Y, ·2Y, ·3Y, ·4Y and so on)

Rotation on z-axis (Z,...

Slicer Notation]]>

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]]>

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]]>

In previous works, Mr. masonjones calculated the god's algorithm for sq1 in twist turn metric[1]. And Mike Godfrey solved all odd-permutation cube-shape positions and found that there're at least 12 positions...

Square one can be solved in 31 moves in face turn metric]]>

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]]>

Megaminx Last Layer]]>

Optimal 3x3x3 solvers, Korf and Kociemba questions]]>

1F1 1F2 1F3

2F1 2F2 2F3

3F1 3F2 3F3

Facelets on F face (7×7×7 cube)

1F1 1F2 1F3 1F4 1F5 1F6 1F7

2F1 2F2 2F3 2F4 2F5 2F6 2F7

3F1 3F2 3F3 3F4 3F5 3F6 3F7

4F1 4F2 4F3 4F4 4F5 4F6 4F7

5F1 5F2 5F3 5F4 5F5 5F6 5F7

6F1 6F2 6F3 6F4 6F5 6F6 6F7

7F1 7F2 7F3 7F4 7F5 7F6 7F7

Fixed center: 4F4

Obliques: 2F3, 2F5, 3F2, 3F6, 5F2, 5F6, 6F3, 6F5

We can describe parts of the cube...

Multi-Purpose Naming System]]>

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]]>

tl;dr: 143 OBTM 141 OBTM 135 OBTM (2017-10-31).

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 this older thread with move...

5x5x5 OBTM upper bound]]>

I have algebra problem. Suppose i want to generate random state on cube with given condition: there must be 14 targets for edges.

What do I want this for? I'm working on something like conditional scrambler, which for input conditions like "2 corners twisted+ one edge twisted+over 10 edge targets" will output me scramble...

Conditional random cube state for given number of targets]]>

Does this account for that fact that the center cubes never move and that the corner cubes will never take up edge positions? Is there a guide to the math anywhere?]]>

My first...

Most Efficient Way to Digitally Store CubeStates?]]>

Hello again. I am back with another EO-solved LL variant that tugs the pareto front lower still, albeit leveraging some cheap commutator tricks. It is called...

As you can tell, [SIMPLE] is a modern version of the 'officially' unpublished LL approach from the Snyder...

[SIMPLE] LL Variant (Revamped 'Fish & Chips')]]>

Random Turn Sequence vs De Novo Random Cube]]>

Q. 1: Given two algorithms, ( we shall notate these 'A.1' and 'A.2' ), and their respective cycle lengths, ( which shall be notated as so: 'C(A.1)' and 'C(A.2)' ), is it possible to work out the cycle length of the concatenation of the two formerly mentioned algorithms, without allowing access to a cube so as to try it out by the 'brute force method' ? ( I.e., given data...

Finding the Cycle Length of A Given Algorithm]]>

- Bottom up: where the best step of the method is nearer the start so there are many ways to finish the method after the best steps.
- Examples include CFOP (where F2L is the core idea), SSC (<20 moves for the first phase) and ZZ...

Top down vs Bottom up method development strategies]]>