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?]]>

1) Where I can find 1LLL? It should be only 28 cases

2) Where I can find few moves syrategy or database algortihms? (In the Wiki section I have not found this material)

Thanks]]>

I'm searching about the number of different combinations that can origin from start position after X moves

I ask also where to download a software that calculate

About cube combinations and calculators...]]>

So the steps for the method are EO, CP, 2-gen left block, 2-gen right block, 2GLL

However, CP recognition is based solely on brute force, which is why this is an experimental method. Here are the...

ZZ-XD Experimental Method]]>

How do they find it?

Are they specially intelligent?

Just by a brute force process?

With complex mathematics?

With computers?

A mix of all those methods?

I guess they try simple movements and annotate how every piece changed.

Later they try to compose several of these movements and try to see if it can be reduced in some way to get the same result.

And then they try to find...

Finding algorithms to solve mechanical puzzles in general?]]>

Also, I'm completely...

Applications of integration applied to Rubik's cubes]]>

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]]>

I know some like R U R' U'

I also figured that by merging them, I could get the same effects. e.g., [R U R' U'] [R' F R F'] that gets...

"looping" algorithms]]>

You need 2 T-Perms, to get to were you started. You need 6 sexy moves to get to where you started. And so on and so forth. But what is the longest of those cycles and how to calculate that?

I assume, that the longest cycle would be a sequence which moves all of the sides.

I should clarify that I'm talking about 3x3 in normal HTM metric.

BTW.: A few years ago i saw a website on which you can type moves and it gives you the cycle number. Is this website still up? I can't find it anywhere.]]>

Taking data from this site for the 2x2x2

Taking data from cube20 and making a similar...

Predicting God's Number for Higher Order Cubes]]>