and looks very similar to the generating function in h-w metric which is
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.
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.
I spent a fair amount of effort documenting it. Any feedback is
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.
I've added a link to Martin's indexed cube lovers archive. Also searches for non-authenticated users will now work.
Hello all. I am new on this great forum. My first post is about Twenty-Four puzzle, larger version of classic Fifteen. I walked around sliding tile puzzles for quite some time. At some point I decided that what I have is too much for me alone, but enough to write about it here.
Many small puzzles have been solved long ago. There is some information in OEIS: A151944 (about MxN puzzles), A087725 (about NxN puzzle). AFAIK largest solved STP is 4x4 puzzle (classic Fifteen). It was known that 80 single-tile moves required and sufficient, and recently Bruce Norskog wrote on this forum about 43 multi-tile moves.
When solving the void cube one encounters odd position parity positions as the cube approaches being solved. The last step for me is to solve the Up face corners and this is where I encounter odd permutations. Corners first solvers may encounter an odd permutation of the Up face edges. The question is what is the shortest maneuver which will convert an odd permutation of the Up face corners into an even permutation of the Up face corners leaving everything else unchanged. This is regardless of the effect on the corner twist. Likewise, what is the shortest maneuver which will convert an odd parity up face edge permutation to an even parity permutation regardless of the edge flip?