cube files
Indexed Cube Lovers Archive
3x3x3 edges only calculations restored
Submitted by cubex on Sat, 07/27/2013 - 13:01.I restored Tom's 3x3x3 edge only calculations from 2004 back to the God's Algorithm Calculations file. It was the waybackmachine to the rescue this time. Somehow the newer version of the file was overwritten. Hopefully it will be updated again soon.
3x3x1 rubik square is isomorphic to ( U2, D2, F2, B2 ) cube subgroup
Submitted by cubex on Sat, 06/29/2013 - 14:02.I hacked up a quick simulator for the 3x3x1 Rubik's Square today and I noticed that the number of positions at each level was the same for the ( U2, D2, F2, B2 ) subgroup of the normal 3x3x3 cube.
Analysis of ( U2, D2, F2, B2 )
------------------------------
Level Number of Positions
0 1
1 4
2 10
3 24
4 53
5 64
6 31
7 4
8 1
---
192
Everyone agree? I'm not sure if this has been pointed out before.» 2 comments | read more
Square subgroup in QTM
Submitted by mdlazreg on Thu, 03/28/2013 - 19:44.The square group analysis in HTM is as follow :
Analysis of the 3x3x3 squares group
-----------------------------------
branching
Moves Deep arrangements (h only) factor loc max (h only)
0 1 -- 0
1 6 6 0
2 27 4.5 0
3 120 4.444 0
4 519 4.325 0
5 1,932 3.722 0» 3 comments | read more
Subgroups using basic moves
Submitted by mdlazreg on Wed, 03/20/2013 - 20:20.In QTM, the whole cube is generated using U,D,R,L,F,B moves.
If we drop some moves we end up with some subgroups. The subgroups are:
I know the depth table for subgroups 1) 2) 3) and 4):
The subgroup 1) generated by "no move", has the following obvious table:
If we drop some moves we end up with some subgroups. The subgroups are:
1) I [the identity] 2) U 3) U,D 4) U,F 5) U,D,F 6) U,F,R 7) U,D,F,B 8) U,D,F,R 9) U,D,F,B,R
I know the depth table for subgroups 1) 2) 3) and 4):
The subgroup 1) generated by "no move", has the following obvious table:
Moves Deep arrangements (q only)
0 1
------
1
The subgroup 2) generated only by the move U, has the following table:» 12 comments | read more
Symmetry Reduction of Coset Spaces
Submitted by B MacKenzie on Fri, 02/22/2013 - 22:44.Having repeatedly shot myself in the foot by mishandling the symmetry reduction of coset spaces, I finally sat down, laid out the math and put together a set of notes on the matter. These notes follow.
Coset Spaces
Solving Rubik's cube either manually or by computer usually involves dealing with coset spaces. A group may be partitioned into cosets of a subgroup of the group:
g * SUB where g is an element of the parent group and SUB is a subgroup of the parent group
» 28 comments | read more
RUF Group Enumeration
Submitted by B MacKenzie on Fri, 02/22/2013 - 22:39.I recently bought a new computer and wanted to put it through its paces. I dusted off my RUF three face coset solver and spruced it up a bit. Since I now have three iMacs in my household connected on an airport network, I rewrote the program using a server–client model. With this I can have all three computers working on a problem in parallel with as many as 14 cores. With these tools I have extended the enumeration of the three face group out to twenty q–turns:
Three Face Enumerator Client Fixed cubies in subgroup: UF, UR, UB, UL, DF, DR, FR, FL, BR. 92,897,280 cosets of size 1,837,080 Server Status: Three Face Group Enumerator Sequential coset iteration Enumeration to depth: 20 Snapshot: Friday, February 22, 2013 9:28:02 PM Central Standard Time Depth Reduced Elements 0 1 1 1 1 6 2 4 27 3 12 120 4 51 534 5 213 2,376 6 914 10,560 7 4,038 46,920 8 17,639 208,296 9 78,234 923,586 10 344,175 4,091,739 11 1,524,115 18,115,506 12 6,722,358 80,156,049 13 29,739,437 354,422,371 14 131,158,304 1,565,753,405 15 578,971,538 6,908,670,589 16 2,546,820,524 30,422,422,304 17 11,174,670,698 133,437,351,006 18 48,528,827,222 579,929,251,620 19 205,901,170,504 2,459,821,160,421 20 814,027,054,726 9,731,195,124,049 Sum 1,082,927,104,708 12,943,737,711,485 92,897,280 of 92,897,280 cosets solved
Back from the Brink
Submitted by cubex on Wed, 02/06/2013 - 07:34.Well, the server had a hard drive failure and I decided that it was time for an operating system upgrade. Unfortunately in the last 9 years everything had changed, e.g. the new versions of php and drupal and mysql were all incompatible with the old versions, and in various ways.
You can imagine my horror when I realized just how much work would be involved in salvaging the forum and make it usable again. I thought all I could do is make the drupal mysql file available to the web and figure out a way of upgrading later.
Finally as a last ditch effort I remembered the Ultimate Boot CD which has a hard drive cloning program and it was able to copy all the sectors still readable to another hard drive. The fact that the critical files were readable and there were multiple kernels bootable on the old failing hard drive was enough to get the server to at least boot, and I was able to restore the last missing files from another backup.
You can imagine my horror when I realized just how much work would be involved in salvaging the forum and make it usable again. I thought all I could do is make the drupal mysql file available to the web and figure out a way of upgrading later.
Finally as a last ditch effort I remembered the Ultimate Boot CD which has a hard drive cloning program and it was able to copy all the sectors still readable to another hard drive. The fact that the critical files were readable and there were multiple kernels bootable on the old failing hard drive was enough to get the server to at least boot, and I was able to restore the last missing files from another backup.
2x2x2 Cube Antipodes
Submitted by B MacKenzie on Wed, 12/12/2012 - 13:34.I have written a GUI NxNxN cube program to which I just added a 2x2x2 cube auto solve function.
To test the performance of the solution algorithm I wanted try it on the 14 q-turn antipodes.
So I did the depth-wise expansion of the group, found the 276 antipodes and reduced them
with M† symmetry. In the context of the fixed DBL cubie 2x2x2 model,
that is the <R U F> group model, M† symmetry classes are formed by
( c * m' * q * m ) where q is a
» 7 comments | read more
How many 26q* maneuvers are there?
Submitted by Bruce Norskog on Sat, 10/20/2012 - 22:17.How many 26q* maneuvers are there?
Well, obviously we can't say for sure, as it hasn't yet been proved that the 3 known 26q* positions (which are symmetrically equivalent to each other) are the only 26q* positions. In another thread, Herbert Kociemba mentioned that there are "many" such maneuvers, but he did not attempt to generate them all (for the known 26q* positions).
I note that 26q* refers to a maneuver that is 26 quarter turns long and that is known to be optimal in the quarter turn metric. It may also refer to a position that requires a minimum of 26 quarter turns to solve. 26q (without the asterisk) refers to any maneuver 26 quarter turns long, but isn't necessarily optimal for the position it solves.
» 22 comments | read more
5x5 puzzle: Comparison between reduction chains (STM, 10000 instances)
Submitted by stannic on Tue, 10/09/2012 - 04:48.The multi-chained approach used in kumi na tano allows to use multiple search chains at the same time. The main advantage is that the best chain can be choosen depending on the instance to be solved, rather than hard-coded into the search algorithm.
For example, the first of the following two 5x5 instances has its leftmost column solved, while second has solved four tiles in top-right corner.
[1] 1 17 9 10 18 18 3 16 4 5 6 0 2 3 8 11 7 17 9 10 11 5 22 7 4 19 2 23 0 21 16 15 20 23 13 6 20 14 12 1 21 19 12 14 24 13 8 15 22 24
We cah use multi-chained approach here. The following two partitioning schemes:
