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I uploaded the xCode project and executable to GITHUB several years ago. See Cube3x3x3 It's an older version and doesn't handle multitasking on symmetrical states as well but comparable to the latest in most respects. I am in the midst of upgrading my solver now. I'm trying to design a...

Thank you. Some of the results shown in the links employ hefty machines with huge pruning tables. My solver makes do with a 1.6 Gb table. In order to fit the table in memory at that time I had to use symmetry reduction which adds a lot of overhead to the search. I should rewrite the code...

Back around 2010, I wrote an IDA optimal cube solver. Both Rokicki and Kociemba had published optimal solver code on the web at that time and my effort was in the same ballpark. A bit slower but not that much. My solver is unusual in that it does not use solving the cosets of the <U, D, R2...

Here's some background info on the representation of the Cubic Symmetry Group. I thought some readers might find it useful.

Here's a test I just ran on my IMac M4 -(void)test3: (NSString *)input { NSDate *start; NSTimeInterval elapsed; NSInteger count; OSG_SYMTAG action[1000][20], state[1000][20]...

No I don't. Could you propose a problem that I could time the solution?

The cubiies of the cube arrive at their positions and orientations by a series of 90˚ rotations about the axes of the cube. The closure of these rotations is the Cubic Rotational Symmetry Group. I represent cube states with a 20 byte list of geometric transforms which will rotate each cubie...

try http://forum.cubeman.org/?q=node/view/516

I don't know what the problem is. If you want you can google "Domain of the Cube Forum" for a link to the site. Then, search for RUF group. There's a lot of neat stuff on the forum.

Back in 2010 I did some work on the three face group and reported my results on the Cube Lovers Forum. Here's a LINK to that post. The above gives results in the qtm, for the ftm see this LINK

I,ve never tried to index the cosets of the <U,D,L2,R2,F2,B2>. subgroup. My own optimal solver is based on indexing the cosets of the subgroup having the UP face solved, which is easy to do: all members of a coset have the same configuration of the UP face cubies. As part of my implementation...

Actually, routines to convert my cubie based rep to a position based facelet pemutation, or a Kociemba like position/orientation rep are straightforward. Michael Reid who wrote the first (as far as I am aware) optimal 3x3 solver introduced a position based facelet perputation rep as a string: a...

I have a unique way to represent a cube state based on the symmetry and geometry of the cube. The cubies are rearranged by 90˚ rotations about the principal axes of the cube. The closure of the group formed by combining 90˚ rotations is the 24 element cubic rotational group. There are 24 ways...

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

Re L U B’ U’ R L’ B R’ F B’ D R D’ F’ One of my favorite patterns. I call it Ouroboros--the snake swallowing its tail. Randelshofer calls it Anaconda.

Remarkable. Does that include the time needed to calculate the depth 15 optimal database? How many CPU years did that take?

Perhaps I misunderstood, but it was my impression that not all cosets were actually solved. Say one has a coset S which has been determined to have a maximum depth of 19. One can define a daughter coset by multiplying all members of the coset by a face turn: t • <S> = S2 <S> • t = S3 These...

One can map the states of the cube to the integers 1 to 43,252,003,274,489,856,000. An integer in that range thus may be deemed a representation of a cube state. If one sets up a computer to count from 1 to 43,252,003,274,489,856,000, on completion the program would have represented all states...

I did a search of the posts on the old Domain of the Cube Forum and found a report of a god's algorithm calculation out to depth 15f. I don't know if anyone has done the calculation out to a greater depth. So as for "seeing" as a computer representation all cube states have been "seen" out to 15f.

12! • 2^11 = 980,995,276,800