Finds the shortest solution to a scrambled 3x3x3 Mixup cube.
The 3x3x3 Mixup cube is a variant of the 3x3x3 Rubik's cube twisty puzzle. It's a super fun puzzle to solve, so you should get one and try to solve it on your own! Unlike a traditional Rubik's cube, the Mixup cube allows a slice to be twisted 45 degrees, which can move edges to places normally occupied by faces, and vice versa.
This program is conceptually based on this optimal solver for the Rubik's cube, which is in turn based on the paper "Finding Optimal Solutions to Rubik's Cube Using Pattern Databases", by Richard E Korf of UCLA.
First, you'll need:
- Linux
- C compiler - gcc and clang are tested, but others should work.
- Make
- Python 3.2 or greater
- Python 3 OpenGL bindings
Compile the C library using Make:
$ make
Right now the only user interface is "viewer.py", which displays the puzzle after a sequence of moves:
$ python3 viewer.py "MU'M'R2"
The program can solve the puzzle when it's not too far away from the solved state. There is still a lot of work to do on optimization. It takes my computer over 3-4 minutes to solve a cube that is 6 away from the solution.
The python interface works well. The only user facing program is "viewer.py", which you can use to manipulate the cube and solve a given state. The interface definitely needs some work to be easy to use though.
The usual Rubik's cube face turns are pretty standard. By default, they are clockwise 90 degree turns. Adding an apostrophe ('), pronounced "prime", means a counter-clockwise turn. Adding a 2 after means a 180 degree turn. These letters also identify the 6 faces of the cube.
- L - Left
- R - Right
- U - Up
- D - Down
- F - Front
- B - Back
The slice moves, M, E and S, are all 45 degree turns, moving pieces from edge slots to face slots and vice versa. They are best explained by picture:
Or if you prefer description:
- M - Middle - Move the slice between L and R faces. The top comes towards the front face. The cubie in the UF slot will now be in the F slot.
- E - Equator - Move the slice between U and D faces. The left comes towards the front face. The cubie in the FL slot will now be in the F slot.
- S - Standing - Move the slice between F and B faces. The top comes towards the right face. The cubie in the UR slot will now be in the R slot.