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Comment by 082349872349872 | Hacker News Reader

There's even a "hyperorganic" Rubik's Cube algorithm: the stereotypical organic algorithm solves the cube layer by layer, only pulling out the fanciest moves to get the last few cubies in place. The hyperorganic algorithm is intensely group theoretic, and starts by allowing any kind of movement, but then cuts it down: from any quarter turns to half turns only, etc. (apparently just at the time no legal moves are left according to the algo, the cube should be solved), and the distinguishing feature is that instead of having clear progress layer-by-layer, it still looks mostly, inscrutably, scrambled until almost the final steps, when it suddenly "crystallises" into a solved cube.

Lagniappe: https://www.youtube.com/watch?v=K-yTrFDHpbw

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I'd mused about how we learn solve the cube in a structured approach and that there perhaps could be a better way and in my mind it would be exactly as you described. Have any humans mastered this approach despite it's hyper organic label?

Depends upon whether or not we count (table-assisted) mathematicians as humans.

The description I remembered comes from 5.6.A (p39) of https://maths-people.anu.edu.au/~burkej/cube/singmaster.pdf (ca.1980)

> [Morwen B. Thistlethwaite's] current algorithm requires at most 52 moves, but ... it may be reducible to 45 with a lot of searching. The method involves working through the following sequence of groups:

    G_0 = <L,  R,  F,  B,  U,  D>
    G_1 = <L,  R,  F,  B,  U^2,D^2>
    G_2 = <L,  R,  F^2,B^2,U^2,D^2>
    G_3 = <L^2,R^2,F^2,B^2,U^2,D^2>
    G_4 = {I}

> Once in G_i, one only uses moves in G_i to get into G_i+1 ... The results for stages 3 and 4 require extensive tables comprising about 500 and 172 entries respectively as well as some preliminary reductions. However MBT has told me today that he has reorganized stage 3 and that it no longer requires such extensive tables.

                           S T A G E
    Max # of moves     1    2    3    4   Total
    --------------     -    -    -    -   -----
    Proven             7   13   15   17    52
    Anticipated        7   12   14?  17    50?
    Best possible      7   10?  13?  15?   45?

compare https://www.youtube.com/watch?v=9rkp29f7QTU&t=24s

EDIT: way more at https://www.jaapsch.net/puzzles/thistle.htm