Comment by 082349872349872

4 months ago

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