Unique 1983 Megaminx Method

[DTCuber]

This is really interesting.

 

[wir3sandfir3s]

I guess I'll also generate some new Algs, maybe they'll be better. Recog doesn't seem too bad.

 

[xyzzy]

lol algs

Spoiler: flip two edges

(R' F R F') (R' F R F') (F' U F U') (F' U F U') (F R' F' R) (U' R U R') (U F' U' F)
(R' F R F') (U F' U' F) (U F' U' F) (F R' F' R) (F R' F' R) (F' U F U') (R U' R' U)
(F R' F' R) (F R' F' R) (R U' R' U) (R U' R' U) (R' F R F') (U F' U' F) (U' R U R')
(F R' F' R) (U' R U R') (U' R U R') (R' F R F') (R' F R F') (R U' R' U) (F' U F U')
(U' R U R') (R' F R F') (R' F R F') (R U' R' U) (F' U F U') (F R' F' R) (U' R U R')
(U' R U R') (U' R U R') (U F' U' F) (R' F R F') (R U' R' U) (F' U F U') (F' U F U')
(U' R U R') (U F' U' F) (R' F R F') (R' F R F') (F' U F U') (F' U F U') (F R' F' R)
(R U' R' U) (R' F R F') (U F' U' F) (U' R U R') (F R' F' R) (F R' F' R) (R U' R' U)
(R U' R' U) (F' U F U') (F R' F' R) (U' R U R') (U' R U R') (R' F R F') (R' F R F')
(F' U F U') (F R' F' R) (U' R U R') (U F' U' F) (R' F R F') (R' F R F') (F' U F U')
(F' U F U') (R U' R' U) (R' F R F') (U F' U' F) (U F' U' F) (F R' F' R) (F R' F' R)
(U F' U' F) (F R' F' R) (F R' F' R) (F' U F U') (R U' R' U) (R' F R F') (U F' U' F)
(U F' U' F) (U' R U R') (F R' F' R) (F R' F' R) (R U' R' U) (R U' R' U) (R' F R F')
(U F' U' F) (U F' U' F) (U' R U R') (F R' F' R) (F' U F U') (R U' R' U) (R U' R' U)

I think the alg in efattah's alg list is nicer despite using one more sledgehammer than optimal. Also, this is the only case that needs seven sledges at the minimum; every other case that doesn't have a 3-cycle of corners can be done with six or fewer.

Spoiler: twist two far corners

(R' F R F') (R U' R' U) (F' U F U') (F R' F' R) (F' U F U') (R U' R' U)
(R' F R F') (U F' U' F) (U' R U R') (F R' F' R) (U' R U R') (U F' U' F)
(F R' F' R) (U' R U R') (U F' U' F) (R' F R F') (U F' U' F) (U' R U R')
(F R' F' R) (F' U F U') (R U' R' U) (R' F R F') (R U' R' U) (F' U F U')
(U' R U R') (R' F R F') (U F' U' F) (U F' U' F) (F R' F' R) (U' R U R')
(U F' U' F) (F R' F' R) (U' R U R') (U' R U R') (R' F R F') (U F' U' F)

Spoiler: twist two adjacent corners

(R' F R F') (R' F R F') (F' U F U') (R U' R' U) (R U' R' U) (U F' U' F)
(R' F R F') (U F' U' F) (R' F R F') (R U' R' U) (F' U F U') (R U' R' U)
(F R' F' R) (F' U F U') (F R' F' R) (U' R U R') (U F' U' F) (U' R U R')
(U' R U R') (U' R U R') (U F' U' F) (F R' F' R) (F R' F' R) (F' U F U')
(F' U F U') (R U' R' U) (R U' R' U) (U F' U' F) (R' F R F') (R' F R F')
(U F' U' F) (F R' F' R) (F R' F' R) (F' U F U') (U' R U R') (U' R U R')

Spoiler: twist three corners in U

(R' F R F') (F' U F U') (F' U F U') (U' R U R') (U' R U R') (R' F R F')
(U' R U R') (R' F R F') (F' U F U') (U' R U R') (R' F R F') (F' U F U')
(F' U F U') (F R' F' R) (U' R U R') (U F' U' F) (R' F R F') (R U' R' U)
(U F' U' F) (R' F R F') (R U' R' U) (F' U F U') (F R' F' R) (U' R U R')

Spoiler: twist three corners not all in one layer

(R' F R F') (R' F R F') (F' U F U') (F' U F U') (U' R U R') (U' R U R')
(U' R U R') (U' R U R') (R' F R F') (R' F R F') (F' U F U') (F' U F U')
(F' U F U') (F' U F U') (U' R U R') (U' R U R') (R' F R F') (R' F R F')

Spoiler: twist all corners

(F' U F U') (R U' R' U) (F' U F U') (R U' R' U)
(U F' U' F) (U' R U R') (U F' U' F) (U' R U R')

All of these also work on the 3×3×3 as they never break up the blocks surrounding the tripod. I think this might be too strong of a restriction to impose, because then we can use only sledgehammers (which cannot solve a corner 3-cycle) and most of these algs look bad. It'd be interesting to see if "proper" <U,R,F> algs are nicer than these.