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It's either 21 or 22. (See Lower bound for the diameter of the 3-gen subgroup <U,F,R>. Specifically, the posts by @Bruce MacKenzie and @rokicki.) On Jaap's Cube Subgroups page, U, R, F = (7!*3^7/3) * (9!*2^9/2) / 2 = 170 659 735 142 400.

BTW, I just updated that wiki page to link (most) algorithms to cubedb. (So now, the presented algorithms are the same as the animations . . . Sorry for any prior confusion, but I had no choice in the past to provide links to algs in SiGN notation instead of Old WCA, as cubedb didn't exist...

Here's your case and alg animated at Twizzle. (I animate at cubedb for the remainder of the links, because it supports Old WCA notation, where lowercase letters = inner slice turns.) You want to solve the corner and 2 wings for the last F2L slot in one algorithm? If so, I made this PDF back...

Based on what he said here (and the title of this thread), the goal of this method is to not use any existing set of commutators or algorithms (or at least an absolute minimal set). He seems to be okay with using a 4 move 2 2-cycle commutator for the corners and half of a 3-cycle commutator for...

How about an FMC challenge to get more people interested? Challenge: Try to solve the first 3 layers of the 4x4x4 for the following scramble (using EAC v1.0) in the fewest STM that you can, where you follow the solve order (and restriction) of the method. Scramble (in SiGN notation): R D' F2 r...

@Platform , I'm not sure if you can learn anything useful from this thread, but just an FYI. (@Herbert Kociemba made some interesting posts.)

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...

I'm not sure about that (left-to-right moves in a twisty puzzle "algorithm" can be represented as a right-to-left product of permutation matrices perfectly . . . well, the piece permutation aspect—Corner and edge piece orientation is a different story). However, I know of three "phenomena" of...

I think @UnknownCorrespondent would agree with you. (Although I think he, like me, isn't a speedcuber.) Well, you can see from this table that the move optimal algs (BHTM is half turns) that most last layer 2-cycle and 4-cycle wing permutation cases require a similar quantity of moves. I...

@cuBerBruce mentioned here that the rest of the pieces (after a 2x2x3) is completed is at least 18 (not 11) moves. (The example he provided. I guess just put that scramble into CubeExplorer and see that the optimal solution is 18 face turns.) Logically, it will also be at least 18 moves for a...

Petrus?

If "weirdest cube I have seen recently" is acceptable, I just saw this one today on rCubers.

I guess you're referring to the human "reverse scrambling" limit. From what I recall, 7 is the limit for most, but it also depends on the scramble (and of course luck, the person's ability, etc.). The majority of scrambles can be created with 18 moves. I think it would be best if you define...

The following was a response from chat GPT (to a query I made last September) to explain how a specific single dedge flip parity algorithm works. (Most people won't get it, but bullet #1 is the funniest part to me.) Edit: Here's the post where I derived that algorithm. (Includes an...

I hope no one ever considers using that for a speedsolving alg! 😅 And its single parity counterpart is even longer! (by 3 STM) r U' M' U M' U' M' U' M Uw2 r Uw2 U' M' U2 M' U M U2 M U M' U M U M' U' l' (Same post of origin.) But yeah, you got the point. It's just an alg to "illustrate the...

@Renslay , I can't claim that it's possible for someone to modify their custom solver to modify (and improve) on this, but algs like this do exist: r' U M' U' M' U M' U M Uw2 l' Uw2 M' U M U' M' U M' U M U2 M' U2 r Post of origin Clearly that (double parity) alg can contain 1 inner slice turn...

Have you tried this alg too? Lw Rw U' 2R U' F2 U 2R' U' x U2 Rw' U2 2R' U2 Lw U2 Rw2 x

As I wrote in this recent rCubers post, OLL parity algorithms which preserve the centers are 13 half turn moves (minimum). So we can only hope that structure (and inner slice turn count) are better in some algorithms than the standard ones. You could convert 4 of the 7 inner slice turns in my...