Is there 1lll for megaminx?

[KP_2085]

I know it's completely impracitcal at there is already I think 517 algs for 2lll but I'm just curious, and if it is a thing, how many algorithms are there for it?

 

[ProStar]

To my knowledge there has been no work done on Megaminx 1LLL. I won’t try my hand at creating the equation to count the number of cases, but it’s safe to say the number is well into the thousands. Here’s the wiki page on Megaminx LL:

Megaminx LL - Speedsolving.com Wiki

 

[Jorian Meeuse]

If I had to guess it would be
1/25 x (1/2 x 5!)^2 x 6^4 = 186624
but that might very well be wrong, I'm no expert on megaminx and I don't know well how it behaves with symmetry and stuff.

 

[Deleted member 27249]

I want a file for 1LLL Mega for create a guide to solve Mega with Platform.
Creation double block 1x1x3 with one Alg or create One block and second block in 2look and in the next solve these case.
I Need of this file because my method Platform for Mega is incompleted.
For 3x3 I created Algs manually but for the mega it is more difficult.

 

[OreKehStrah]

There is a very very large amount of algs for 1LLL. The optimal move count in 3,4 and 6 get has been found recently thanks to Tomas Rokicki. I have attached an image of the distribution. It looks strangely similar to optimal 3x3 move count distributions lol. This was found in part of the work for making a better Megaminx LL scrambler.

I have genned ALL of Megaminx ZBLL in RU gen and ZBLS in RUFL gen using the batch solver. I keep meaning to make a post about that but haven't yet. There are 11,520 ZBLLs and 695 ZBLS cases. I'll probably get around to making a post in the next couple days with links to the files containing the algs. I should note that they contain multiple algs for each case and are NOT sorted for what algs are good or bad. It was just to have the whole set documented. I am working on a more curated 1LLL for cases that would actually be good to learn. Megaminx ZBLL can be pretty awful to recognize, especially since people struggle with recognizing some of the PLLs quickly. When EO is solved, you would be better off learning the 2 thousand OCLS cases (which I also penned lol) then doing PLL than trying to learn the 11.5k ZBLLs.

If anyone is interested in Mega LS/LL stuff feel free to message me.

 

[CasualGigaminxer]

There are 81 (3^4) possible states of corners twisting in Megaminx.
There are 16 (2^4) possible states of edges flipping in Megaminx.

Thus, there are 1296 states of the orientation of last layer (OLL) in total (including OLL skip).

There are 60 (5!/2) possible states of corners permutation in Megaminx.
There are 60 (5!/2) possible states of edges permutation in Megaminx.

Thus, there are 3600 states of the permutation of last layer (PLL) in total (including PLL skip).

Most of the LL cases can have up to 25 variations. Except the following 10 PLL cases where each of them can have only 5 variations:

1) O (PLL skip)
2) H1+
3) H1-
4) H2+
5) H2-
6) N2+
7) N2-
8) X1
9) X7+
10) X7-

Thus, the 3600 states of the PLL cases can be reduced to 151 algorithms and 1 PLL skip because:
(142 * 25) + (10 * 5) = 3600.

1296 * 3600 = 4665600 is the number of all possible 1LLL states.
There are 4665600 - 3600 = 4662000 OLL cases because the LL skip and the PLL cases have been excluded.

Then, we can have 4662000 cases / 25 variations = 186480 distinct full non-PLL 1LLL cases.

All of these 186480 cases are reduced to 259 full OLL cases in 2LLL because we consider only the states of the grey color pieces.
186480 / 259 = 720 means that there can be the algorithms like 01A_001, 01A_002, and so on until 53E-_720.

Finally, we have 186480 non-PLL 1LLL cases, 151 PLL cases, and 1 LL skip.

The total number of 1LLL algorithms for Megaminx is supposed to be 186631 algorithms (or 186632 cases with 1LLL skip included).