Development of a megaminx solver

[Christopher Mowla]

Hey guys, I have a 53-move superflip solution.

• That's actually have a 51 btm superflip solution!
  • You forgot to merge two moves on 2 occasions.
  • Two of the turns are both parallel and turned in the same direction, so some may count that as 1 block ("slice") turn—I put the 2 parallel moves in parenthesis in the link. (It's 50 moves, according to that pattern database website, despite showing as 51 moves at Twizzle.)
• Since your alg isn't "superminx safe" (it twists some centers), then instead of comparing it with the alg list I provided earlier, we compare it with this one. Clearly the shortest solution currently listed is 49 btm. (By @rokicki.)
• Just 1-2 moves longer than the shortest (non-pure) superflip alg found? Impressive!

 

[ananasclassic]

Just 1-2 moves longer than the shortest (non-pure) superflip alg found? Impressive!

For context, I had previously found a 47-move superflip solution in FTM/BTM, but my best QTM solution was 54 moves, one move longer than Ivan’s.

 

[Ivan Litvak]

Hello guys, got a superflip solution of length 51 in QTM. Here it is, ananasclassic will probably fix it.
rokicki, what do you think?

puzzle_solved=1 puzzle_id=0 seconds=22600.2 solution_length=51 solution=-U.D.-DL.-FL.-L.-FL.-F.-FL.-FR.DL.-FL.-D.-FL.BL.-DR.-R.L.-FL.F.FL.-F.-DR.-FR.-FL.-D.-FL.-DL.-FL.-FL.U.FR.FL.L.-BL.FL.FL.-B.D.-DL.-D.DL.-L.-BL.-U.-BR.DR.-B.-DL.-L.FL.B

 

[rokicki]

Can you edit your message to turn that solution into a proper URL with proper moves?

In any case, if this works, that's pretty good! I mostly care about face turn metric, but a 51-QTM solve would be pretty impressive too.

 

[ananasclassic]

Hello guys, got a superflip solution of length 51 in QTM. Here it is, ananasclassic will probably fix it.
rokicki, what do you think?

puzzle_solved=1 puzzle_id=0 seconds=22600.2 solution_length=51 solution=-U.D.-DL.-FL.-L.-FL.-F.-FL.-FR.DL.-FL.-D.-FL.BL.-DR.-R.L.-FL.F.FL.-F.-DR.-FR.-FL.-D.-FL.-DL.-FL.-FL.U.FR.FL.L.-BL.FL.FL.-B.D.-DL.-D.DL.-L.-BL.-U.-BR.DR.-B.-DL.-L.FL.B

Link
First two turns can be merged into the one BTM turn, but I don’t remember the exact notation for that.

 

[Renslay]

Link
First two turns can be merged into the one BTM turn, but I don’t remember the exact notation for that.

It's y 2U'

 Twizzle link 

2U' DL FL L FL F FL FR DL' FL D FL BL' DR R L' FL F' FL' F DR FR FL D FL DL FL FL U' FR' FL' L' BL FL2' B D' DL D DL' L BL U BR DR' B DL L FL' B'

EDIT: since it is the very first move, the y can be omitted.

 

[ananasclassic]

I’m finally back with something interesting: a 44-BTM superflip solution.

 Twizzle link 

2U2 2BL 2R2' 2U2 2BR 2U2 2R 2BR 2L2' 2F' 2L 2U2 2BR' 2U 2F 2U' 2R' 2F2' 2R 2L' 2U' 2L 2U2 2BR' 2R2 2BR 2R' U R' 2U L FL2' D F2' FL2' F2 FL' D2 FL2' L' U B 2L' F2 Uv2 Fv

Training the BTM model was unexpectedly difficult, unlike the QTM and FTM models, but I finally managed to get it working after two weeks of failed attempts.

 

[ananasclassic]

I also keep trying to solve the pure Megaminx, but I still can’t train a model that can solve it at all, and I don’t understand why.

 

[ananasclassic]

I have also put together a catalogue of my improved Megaminx pattern algorithms.

I used Walter Randelshofer’s Megaminx pattern collection as the starting point:
https://www.randelshofer.ch/rubik/megaminx/

So far, I have improved 218 out of 334 patterns, which is about 65.3% of the entire catalogue. Another 76 results tie the previously published algorithms, while 40 are currently longer.

Overall, the total length of the catalogue has been reduced from 10,250 BTM to 8,801 BTM, saving 1,449 moves in total.

Some of the more interesting results include:

• 4 Propellers: 58 → 25 BTM
• Superfliptwist: 76 → 44 BTM
• 4 Stars: 50 → 25 BTM

You can browse all of the results here:
https://ananasclassic.github.io/improved_megaminx_patterns/

This is the interactive catalogue. It contains all 334 patterns and lets you search and browse through them. Each pattern page shows the previously published algorithm, my personal-best solution, an FTM-focused solution, the move counts, and an interactive 3D Megaminx preview. There are also direct links for opening each algorithm in Alpha Twizzle.

The complete source code and dataset are available here:
https://github.com/AnanasClassic/improved_megaminx_patterns/tree/main

The GitHub repository contains the website source code and the full machine-readable pattern database, including the old and new algorithms, their lengths, pattern names and codes, author information, and Twizzle links. This may be useful to anyone who wants to analyse the results or reuse the data in another Megaminx project.

Ivan Litvak and I are also planning to rerun some of these searches with significantly wider beam widths. Our previous experiments suggest that increasing the available computational power can produce further improvements, so there is a good chance that at least some of the current results can still be shortened.

These results are not necessarily optimal; they are simply the shortest solutions I have found so far. I plan to keep working through the catalogue and trying to improve the remaining patterns. I am also interested to see whether anyone can shorten some of these solutions further.