## 5x5x5 Solving Programs: The list is growing

Submitted by NoLongerUnsolve... on Sun, 06/05/2016 - 22:06.## New 3x3x3 Corners Data Including Centers

Submitted by NoLongerUnsolve... on Sat, 06/04/2016 - 08:55.I decided to create a database that:

A. requires no single point of reference

B. contains all 24 possible rotated states of the cube's corner arrangements

C. measures the distance the corners are from the solved state with respect to the fixed centers

## IP address for forum changed to 69.165.220.244

Submitted by cubex on Fri, 05/06/2016 - 23:57.My upstream has changed my ip address so now the numeric ip is 69.165.220.244. All the links should work as before once all the dns changes have propagated.

## Cube archives changed

Submitted by cubex on Sat, 03/19/2016 - 07:40.## Confirmation of Results for Edges Only Cube, Face Turn Metric, Reduced by Symmetry

Submitted by Jerry Bryan on Tue, 02/23/2016 - 12:42.Even though it's only confirmation of some rather ancient results, I would like to report that I have succeeded in replicating Tom Rokicki's 2004 results concerning the edges only cube in the face turn metric reduced by symmetry. My goal was not really to solve that particular problem. Rather, it was to use that problem as a way to prototype some ideas I have had for improving my previous programs that enumerate cube space.

The base speed of my program is that I am now able to enumerate about 1,000,000 positions per second per processor core when not reducing the problem by symmetry, and I am now able to enumerate about 150,000 symmetry representatives per second per processor core when reducing the problem by symmetry.

## Refining Bruce Norskog's 4x4x4 five stage analysis

Submitted by Clement Gallet on Fri, 12/11/2015 - 08:03.Except for the last stage where centers need to be solved, every other stage needs to place 8 centers from a single axis (RL, FB or UD centers) in their correct faces (RL, FB or UD faces), in one of the 12 positions that can then be solved using only half turns. However, as pointed by Shuang Chen in his analysis, we don't need to store the exact colours of centers but only if two centers have the same or different colours. This reduces the number of center coordinates by 2.

Also, as opposed to the 3x3x3, 4x4x4 does not have fixed centers, which allows us to do more symmetry reduction. I'm representing a sym-coordinate as:

s1 * g * < H > * s1' * s2'

where g * < H > is a coset, s1 and s2 are symmetries from subgroups S1 and S2 of the group M of symmetries of the cube. s1 is the usual conjugated symmetry, and s2 correspond to a rotation of the cube, which is possible on the 4x4x4. Using carefully chosen subgroups S1 and S2 for each stage, more symmetry reduction is achieved. I will be using the Schoenflies symbols for subgroups of M in the following.

## Router Problem

Submitted by cubex on Mon, 08/31/2015 - 11:15.Sorry about the outage. Just letting everyone know that the forum is still alive :)

Mark

## 4x4x4 upper bounds: 57 OBTM confirmed; 56 SST and 53 BT calculated.

Submitted by rokicki on Tue, 03/03/2015 - 02:14.I have also calculated, with the same code, results in two other metrics: SST (single slice turn) and BT (block turn). The final results lower the upper bounds in these metrics to 56 and 53 (respectively).

The sequence of subsets chosen is identical to that used by Chen. The maximum distance for each stage, the sum, and the current lower bound is shown here:

## What is God's Number for WrapSlide?

Submitted by Alewyn Burger on Wed, 10/22/2014 - 08:36.First let me describe WrapSlide:

The main puzzle is a 6x6 grid of colored tiles which are separated into four quadrants of 3x3 tiles. When it is unmixed all the tiles in a quadrant have the same colour. A move consists of sliding either the top, bottom, left or right two quadrants of tiles 1 to 5 units horizontally or vertically. Stated differently, a move consists of sliding either the top, bottom, left of right half (consisting of 3 rows or 3 columns) relative to the other half, thus giving 4x5 possible moves to choose from. As with Rubik's cube the puzzle is to return it to its unmixed state after it is scrambled. (For the unmixed state we don't care which color goes into which quadrant)

## The Void Cube to 13q

Submitted by B MacKenzie on Fri, 10/03/2014 - 19:12.Breadth First Enumeration 2014-09-27 19:58:23.094 VoidCubeClient[508:5903] 0 1 1 2014-09-27 19:58:23.095 VoidCubeClient[508:5903] 1 1 12 2014-09-27 19:58:23.099 VoidCubeClient[508:5903] 2 5 114 2014-09-27 19:58:23.101 VoidCubeClient[508:5903] 3 17 1,068 2014-09-27 19:58:23.105 VoidCubeClient[508:5903] 4 130 9,951 2014-09-27 19:58:23.133 VoidCubeClient[508:5903] 5 1,018 92,592 2014-09-27 19:58:23.333 VoidCubeClient[508:5903] 6 9,204 860,852 2014-09-27 19:58:25.033 VoidCubeClient[508:5903] 7 83,789 7,991,856 2014-09-27 19:58:40.300 VoidCubeClient[508:5903] 8 774,323 74,114,319 2014-09-27 20:01:03.984 VoidCubeClient[508:5903] 9 7,159,250 686,774,712 2014-09-27 20:25:47.908 VoidCubeClient[508:5903] 10 66,273,224 6,360,091,030 Coset Enumeration Void Cube Model 1.0 Group: R, U, F, TR, TU, TF Coset Base Subgroup: Subgroup with solved corner cubies and the UF and UR cubies in the solved position regardless of orientation. 484,989,120 cosets of size 7,431,782,400 Coset Symmetry Reduction: Oh+ Cosets solved since launch: 3,429,943 Average time per coset: 0:00:00.068 Server Status: Void Cube Enumerator Server Enumeration to depth: 13 Snapshot: Friday, October 3, 2014 at 6:56:34 PM Central Daylight Time Depth Reduced Elements 0 1 1 1 2 12 2 18 114 3 50 1,068 4 447 9,951 5 2,008 92,592 6 19,000 860,852 7 124,184 7,991,856 8 1,136,806 74,114,319 9 9,028,936 686,774,712 10 82,411,850 6,360,091,030 11 711,657,402 58,868,124,048 12 6,507,640,604 544,562,369,684 13 58,275,341,089 5,033,855,951,932 Sum 65,587,362,397 5,644,416,382,171 484,989,120 of 484,989,120 cosets solved Elapsed Time: 0:12:14:50

This work was performed using the <R, U, F, TR, TU, TF> group model. This model was discussed in a previous thread. It must be pointed out here that the <R, U, F, TR, TU, TF> metric is exactly the same as the <R, U, F, L, D, B> metric since TR = L , TU = D and TF = B on the void cube. It makes no difference if the left face is rotated holding the rest of the cube rigid or if the left face is held rigid and the rest of the cube is rotated in the opposite direction, the rearrangement of the cubies is the same. If a distinct state of the void cube is at say depth 13 in the <R, U, F, TR, TU, TF> metric it will be at depth 13 in the <R, U, F, L, D, B> metric.