The search for a 21f, an idea for some candidates

There is a unique Rubik cube position maximally far from Start *PROVIDED*
you only look at edges and ignore corners - it was found by J.Bryan and
is all edges flipped in place, composed with a mirror reflection of the whole

That suggests, taking this one edge position and exploring all possible configurations
(there are about 3 million) of the 8 corners to get 3 million cube positions.
If you are seeking a cube configuration with 21f or more distance to start,
these 3 million candidates seem tolerably likely to include a winner.

Because 3 million is a lot of searching, you might try a cheaper approach like just
searching for local distance-increasing changes within the 3 million...

Warren Smith

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This is already done. See Som

This is already done. See Some more interesting groups from Tom Rokicki.


Rokicki already had done my suggestion (what he calls "pons asinorum"
is a "central inversion of the 12 edges") and found that no 21f's but
a lot of 20f's result.

I suppose he could now try some of the other edge-positions besides the
4 he did try (the pon-asinorum-superflip was the unique one I suggested
because it is uniquely furthest from start, but you could try a few nearly-furthest
but not furthest edge-positions too; might as well if it only takes a few hours)?

Actually, the cosets I'm solv

Actually, the cosets I'm solving now (inspired by Silviu; read the top few articles) are much larger and run faster (in terms of solutions per second) so I'm focusing on those. Still no 21f*'s, and I've solved more than 1 in every 50,000 positions *total*---many trillions of positions.