cube files
Indexed Cube Lovers Archive
Regularities in maximum WD values
Submitted by stannic on Sat, 01/14/2012 - 15:26.Regularities in maximum WD values
This post is about any mathematical laws inside the Walking Distance heuristic. It seems like WD is not just puzzle to be computed. Maybe the whole WD heuristic is some math structure.
» 6 comments | read more
A Hamiltonian Circuit for the 2x2x2
Submitted by Bruce Norskog on Mon, 12/26/2011 - 13:33.I have found a Hamiltonian circuit for the 2x2x2 cube group (3674160 elements). I have posted the solution on the speedsolving.com forum. Link: http://www.speedsolving.com/forum/showthread.php?34318
Number of canonical move sequences for nxnxn Rubik's cube in q-w metric
Submitted by kociemba on Mon, 12/26/2011 - 12:22.Quarter turn metric is more difficult to handle than h-w metric, because the 180 degree turn has to be counted as two moves, which gives some issues with an recursive approach. I did not believe it was possible to get a simple formula here. I was very surprised, that the result was a simple generating function for the number of canonical sequences in q-w-metric. It is
gfq[n_,x_]:=3/(6-4(x+1)^(2(n-1)))-1/2
and looks very similar to the generating function in h-w metric which is
gfh[n_,x_]:= 3/(6-4(3x+1)^(n-1))-1/2
» 3 comments | read more
Number of canonical move sequences for nxnxn Rubik's cube in h-w metric
Submitted by kociemba on Sun, 11/20/2011 - 17:22.In h-w metric, a move of the nxnxn cube is a 90 or 180 degree turn of a face together with 0..n-2 adjacent slices. When counting the canonical move sequences the commutativity of the moves on one axis has to be taken into account. The number of canonical move sequences can be computed quite elegantly using matrices
» 6 comments | read more
Interchanging two faces
Submitted by brac37 on Fri, 11/11/2011 - 12:24.Hello all,
Just a question for fun. Suppose you have a Rubiks cube and you want to interchange two faces? How many stickers need to be moved?
Distinguish between opposite and adjacent faces and between using a screwdriver (for disassembling) or not, so you get four answers.
Next, do not read any further before adding those four answers to obtain a single answer.
Some 3-color cube results
Submitted by Bruce Norskog on Wed, 11/02/2011 - 22:57.The Rubik's Cube can be simplified by using only 3 colors instead of the usual six colors. Generally, opposite faces would share the same color, and that is the convention I assume here in talking about a 3-color cube.
Kunkle/Cooperman showed that a scrambled cube can always be brought to a position within the squares group within 16 moves. This puts an upper bound for God's number for the 3-color cube at 16. It is also well-known that the cube can be put into the <U,D,L2,R2,F2,B2> group in 12 moves. That puts a lower bound on God's number for the 3-color cube at 12. The superflip equivalent for the 3-color cube requires 14 moves according to an optimal 3-color cube solver program I have written. (From solving a million random positions, it appears that about 1.4% of positions of the 3-color cube require 14 moves to solve.) This raises the lower bound for the 3-color cube to 14.
» 17 comments | read more
Source Code for Face Turn Metric 20 Proof Released
Submitted by rokicki on Tue, 10/11/2011 - 12:03.You can find the source code used for the "20" proof at:
http://cube20.org/src/
I spent a fair amount of effort documenting it. Any feedback is
welcomed.
http://cube20.org/src/
I spent a fair amount of effort documenting it. Any feedback is
welcomed.
5x5 can be solved in 109 MTM
Submitted by stannic on Mon, 08/15/2011 - 10:53.Any instance of the Twenty-Four puzzle (5x5) can be solved in 109m (multi-tile moves) or less. My proof consists of several steps. It is possible that there is logical error in this proof, so please check it thoroughly. However, I cannot find errors.
» 20 comments | read more
Clarification on how to contact the admin
Submitted by cubex on Sat, 08/13/2011 - 01:51.To contact the admin of this site send emails to: cubexyz at gmail dot com
I've added a link to Martin's indexed cube lovers archive. Also searches for non-authenticated users will now work.
I've added a link to Martin's indexed cube lovers archive. Also searches for non-authenticated users will now work.
Approximation formula for the lower bounds of nxnxn cube in slice turn metric
Submitted by kociemba on Wed, 08/03/2011 - 17:40.I tried to derive some analytic approximation formula for the lower bound in h-s metric, that is half-turm metric with slice moves for large n. There are 9n possible slice moves for an nxnxn cube, and without using any other relations where would be (9n)^k move sequences of length k. In my simplified model I only used the relations that the 3n slice moves of one axis commute and that there are never two successive moves with the same slice (the latter does not hold in quarter turn metric).
» 3 comments | read more
