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As you can tell, [SIMPLE] is a modern version of the 'officially' unpublished LL approach from the Snyder...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

we will want to see of the NAME OF THE METHOD at the top in caps.

the first thing we want to see is the inputs

i1. ALGORITHM LEVEL. the equation is (avg move count for this step * amount of cases for this step)

if the method has more than one algorithmic step you do this on the next line labeled i1b, then i1c..............

i2. INTUITION LEVEL. for each intuitive step (labeled i2, i2b....). the...

equation based method statistics]]>

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]]>

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]]>

A Winter Variation COLL would be beautiful for ZZ solvers like myself, but a standard WV with ZZ is not bad.

I've used Cube Explorer (although I suck at it) to try to cut down the last slot 1LLL algs as much as possible. but since I have no idea how to use the tool I didn't succeed. I'd love an alg number for that.]]>

A corner piece has three visible facelets, an edge piece has two visible facelets and a centerpiece has only one visible facelet. When talking about the centers I will use the terms "facelet" and "centerpiece" interchangeable....

nxnxn cube solver]]>

The chance you get a cube that can be solved with 10 moves is approximately the same as getting 28 Heads in a row in a coin flip (or 5.37e-07%. See, coin flips are better).

Here's a table:

...

Moves | Flips |

3 color 3x3x3 algorithm thread]]>

it's probably some really silly thing that would be silly to recognize but it seems like an interesting question.

what about 3 look?

I can't really think of a way of finding such a method so i'll let the puzzle theory people find it instead]]>

That's a lot of moves, but imagine if, like for L2E, we could solve L4E in a single alg. This post is about that.

tl;dr:...

5x5x5 last four edges move count]]>

In 2013, @cuBerBruce generated the distance distribution for solving a single face's centres in multiple metrics. I have confirmed the results for OBTM (since my code supports only OBTM).

Code:

total states: 112911876 (112911876 legal) distance 0: 1 nodes distance 1: 12 nodes distance 2: 190...

I was wondering if anybody knows of a presentation of the cube group documented somewhere?

For those of you that don't know, a

G=<A|R>

In the case of the cube group this would...

Does anybody know a presentation of the cube group?]]>