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?]]>

Megaminx Last Layer]]>

When I say "world's best mathematicians," I mean those who are the best in the areas most relevant to cube theory, such as abstract algebra and group theory, combinatorics, other discrete math, etc.]]>

While I'm at it I've calculated lower bounds as follows:

3x3: 3 possible first moves (cw, ccw, 1/2 turn, which face doesn't matter)

15 second moves (the other 5...

Approximating Dodecahedron 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]]>

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]]>

This post gives a simple overview of the different parities that can occur during a reduction solve on 4x4x4 upwards.

Even layered cubes (e.g. 4x4x4 and 6x6x6) have the concept of OLL parity and PLL parity whereas odd layered cubes (e.g. 5x5x5 and 7x7x7) only have the concept of Last Two Edge (L2E) cases.

It may not be immediately apparent how these cases are related so I thought I would try to summarise in simple terms.

Relationship of OLL Parity + PLL Parity + L2E]]>

For n bad edges what's the most optimal rotation to get the least # of bad edges?]]>

tl;dr: 143 OBTM.

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 counts of human solves, reduction can and...

5x5x5 OBTM upper bound]]>

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]]>

Anyway, I was wondering what this would look like on the megaminx. My current vision is that L and R stickers can show up on L and R, U and F stickers can show up on...

Megaminx ZBLL]]>

Some Maths about the Cubominx]]>

Today, I tried a similar calculation with a more modest goal: finding only the possible orders. I believe I have succeeded in this. I started by...

Possible orders of Rubik's Cube positions]]>

And if there's a good website that I just...

Formula for Calculating Positions of a NxNxN Cube?]]>