## There are approximately 700,000,000 distance-20 positions.

Submitted by rokicki on Sat, 11/08/2008 - 14:32.I first wrote a program to select a random coset, and then set those cosets to running, specifying a maximum search ply of 18. This way

## Some observations on the Rubik's Cube Group, its sub-groups and solution algorithms.

Submitted by B MacKenzie on Fri, 10/31/2008 - 17:12.Some observations on the Rubik's Cube Group, its sub-groups and solution algorithms.

When approaching the problem of auto-solving Rubik's cube in my Virtual Rubik program I chose to proceed in a three step process by first solving a 2 x 2 x 2 block using turns of all six faces. Then using turns of the three faces not intersecting the solved block, the block is extended to a 3 x 2 x 2 block, leaving two faces unsolved. And finally the last two faces are solved using just turns of those two faces.

## Enumerating all of 3x3x3 cube space - required performance characteristics

Submitted by Jerry Bryan on Tue, 10/07/2008 - 11:24.I've been playing around with what it would take to enumerate the entire cube space for the standard 3x3x3 cube, using a large number of computers working together. I've come up with what I think is a reasonable approach, a bit past the bare edge of what might be possible with today's technology, but perhaps not too far past. The assumption will be that we want to solve the problem in one year, with all the machines involved in the project fully dedicated to the problem for the whole year.

The following is not a compete description of my proposed approach, but rather is an analysis of the performance characteristics that would be required. There is not much advantage in coming up with an approach that would require billions of years to compute.

## First Post, General Puzzle Solving

Submitted by quadricode on Fri, 09/19/2008 - 02:51.A quick introduction: I'm Robert Smith, I'm 18, and I live in the US. I used to be quite into speedcubing, starting around 2003, but I have since moved into the more "theoretical" aspects of the cube. I also like mathematics, and, fortunately, programming. Anyway, that's that.

I have been writing a "general puzzle solver," whose goal is to be able to solve any (permutation) puzzle with (almost) any method. Quite quickly, we see there are definitely limits to this (e.g., we couldn't solve any scrambled 10x10x10 cube in a single phase). But, if some certain requirements are met, solving any puzzle should be an ability with this program.

## Superflip

Submitted by brunson on Tue, 09/16/2008 - 10:37.Has anyone posited other positions that could be proved to require 20 moves similarly? Has it be postulated that the superflip could be the only position that requires 20 moves?

Thanks,

e.

## U turn sans U turns

Submitted by B MacKenzie on Thu, 08/21/2008 - 22:28.All elements of the Rubik's cube group may be generated using turns of only five of the six faces, say all but the Up face. This suggests a puzzle variant: a cube with the Up center cubie glued fast. Has any work been done on such a puzzle? I played with this a bit today. Here's an U turn macro using no U turns:

B D' F L' F' B D F' R B' L F' D F B' L' F

## Upgraded to apache 2.2.9 and php 4.4.9

Submitted by cubex on Mon, 08/18/2008 - 22:20.Mark

## Twenty-Two Moves Suffice

Submitted by rokicki on Tue, 08/12/2008 - 20:27.This required approximately 50 core-years of CPU time contributed by John Welborn and Sony Pictures Imageworks.

No distance 21 positions were found in this search, despite solving a total of more than twenty-five million billion cube positions.

There is a short article in New Scientist (August 9th edition) on this problem and this result.

The same techniques for the proof of twenty-five moves were used, just on many more computers.

I have found 310 cosets with an upper bound of 18, and about 82,000 with an upper bound of 19 (or less); all the rest have an upper bound of 20 or less.

## Supergroup knowledge

Submitted by rokicki on Fri, 06/13/2008 - 16:07.center facelets.) Have any computer explorations been performed? Any "hard"

positions known? Any coset explorations?

I know Jaap has a supergroup solver embedded in a Java applet. Does anyone else have

any programs?

A start might be an optimal solution length distribution that take a solved cube to a

solved cube, but just change the center facelet twists. But maybe an optimal solver

for the supergroup would just be too slow.

## My diploma thesis - Human method evaluator

Submitted by StefanPochmann on Fri, 05/02/2008 - 14:52.http://stefan-pochmann.info/hume/

Cheers!

Stefan