Remember that Scientific American article about some new permutation puzzles based on simple sporadic groups? There was the M12 puzzle (for which I gave a few hints), along with the M24 puzzle and dotto puzzle. The last two puzzles I described as "ridiculously complicated", but it seems that someone out there has gone and solved the M24 puzzle. You can congratulate Baumann Eduard.
See his solution here
You will also need this table
That's really amazing.
In other news, it was recently proven that at most, 22 moves are required to solve any Rubik's cube. Positions are known that require 20 moves, so we now know that the optimal solving algorithm requires between 20 and 22 moves.