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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.

So since superflip can be solved in 47 moves, and we know by canonical sequences and state counts that there are positions that take at least 48 moves, this proves that superflip is not an antipode on the megaminx.

I bet that was narrated, and "Kelly" should be "Cayley". In any case, the question then becomes, how much of the "secret sauce" is in the "lot of your own code" or the general approach. For instance, if you recognized a particular distance heuristic (some variation of a Manhattan metric, say)...

Personally, I think this is the first major, significant breakthrough in the application of AI to twisty puzzle theory. The 3x3x3 results from the various AI papers are not as impressive since we have conventional optimal and near-optimal solvers that are very efficient. The 4x4x4 and 5x5x5...

That's really phenomenal. The best I was able to do, with huge effort some years back, was 55 moves, so this is a huge improvement. Can you telll us a bit about your approach? Also, what's the best pure solution you can come up with (that's one that preserves center twist; that is, it solves...

For those not following everything: note that the Cayley competition uses quarter-turn metric, not the more conventional face-turn metric, so getting to 80,000 (for something like one thousand positions!) is pretty impressive!

I haven't given this much effort, and probably won't for a while, but that 81,633 is pretty impressive.

This is all very fascinating and I wish I had seen it earlier. The twsearch program has this sort of computation built-in for general puzzles. For instance if I run build/bin/twsearch -C teraminx.tws I get Found 901 canonical move states. D 0 this 1 total 1 D 1 this 144 total 145 br 144...

Here is a possible order that reduces the maximum number of states if you ignore the last phase: U D F B L DR BL FR BR FL R DL 1.0066961655352334986e+68 1,641,669,120,000 U D F B BL R 6.1321502199860667957e+55 640,530,519,552 U F B BL R 9.5735488517783929653e+43 168,782,745,600 U F BL R...

Actually, Ben took the 7595 distance-25 positions in 2gen, reduced them by symmetry and inversion to 1199 distinct representatives. I then solved all of these in U,R,F and found that all of these are solvable in 24 or fewer moves. So yes, we can take two moves off the upper bound.

The 16 26-move antipodes of U,R two-gen can be solved in 24 moves each if you add F. So this can cut one move off the upper bound. Here are the 24-move solutions. U F' R F R2' U2' R U2' R2 U2' F' U R2 U2 R' U2' R U R' U2' R2 F U2' R2' U R2' U' R2' F' U2' F R' U' F' R2' U2 R2 F U2' F' R2' U...

Just take your first 26q solution and conjugate by x to get a solution to your last position: https://alpha.twizzle.net/explore/?alg=x+F+U2+R%27+L+F2+U+F%27+B%27+R+L+U2+R+U+D%27+R+L%27+D+R%27+L%27+U2+D2+x%27 So, clearly, they are equivalent. (They are also equivalent just by inspection...

The two positions you give are just rotated versions of the ones in the files. For brevity the files only include one symmetry representative. But the positions you list above are indeed distance 25, just not new. To see this without any code, just put your scrambles into any visualization...

These are the two already-known distance-25 positions.

I haven't been active here so I missed this discussion. But here's a couple of notes: 1. For canonical sequences and counts, what Herbert describes above is pretty much accurate. The twsearch program includes an implementation that works for many puzzles (including megaminx) with the -C...

A couple of us have been pushing on megaminx superflip for a while. But I'm truly excited about this new megaminx solver, and curious about how it does for this particular position. I don't expect it to be competitive with the solutions on the web page you reference (which took many many days...

How many moves does this take to solve megaminx superflip?

I recommend using twsearch. Failing that, try using the ksolve in my github; that's got a lot of bug fixes and speed improvements for ksolve1.3. But absolutely twsearch is much better than even that version of ksolve. For example, for the def file and scramble you provide, twsearch takes a...

Okay, I found the files I generated for Lars. They are in: http://codercontest.com/firsttwo/firsttwo-#.mov.xz where # ranges from 6 to 19. They are probably not in a format you prefer though so let me know and I can change the format and/or provide more information. They are just raw...

Wow, under a move per cubie! That's a lot better than the other huge-cube solvers I'm aware of (but I think they generally use a lot less memory and run a lot faster). Can you give a move-count breakdown for the various phases and subphases?