Message #421

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] tag, you’re it!
Date: Sat, 08 Sep 2007 17:51:51 -0700

What can I say Roice? On one hand I knew that you would never rest while
someone else held the record for shortest 3^4, but on the other hand it
really does seem like we’re pushing up against some sort of hard limit
for this method. I never expected to see sub-500 twist solutions, and
now with sub-300 solutions, well, I guess I’ll just stop trying to
predict these things. I stand completely in awe of all you guys.

Congratulations, Roice.
-Melinda

Roice Nelson wrote:
>
> Hey guys,
>
> Here is my next entry for the shortest competition, using the same
> starting state as Remi. It totaled 298 moves, and I hope it will
> really give Remi and others a run for their money!
>
> In thinking about the theoretical bounds of this method, I thought
> averaging 2^(C-1) moves for each piece type might be doable (2 moves
> for 2C faces, 4 moves for 3C edges, and 8 moves for 4C corners). This
> would put one at 304. But I thought it’d be sweeter to cross the 300
> barrier, which would also reduce the record length by over 10%. I
> barely made it, and had to backup and retry the last 3 sequences
> to squeeze away an extra preliminary move (I was a little disappointed
> earlier today as I thought 300 was going to be it this time).
>
> There was nothing fundamentally new in my approach. I thought about
> trying to do some coding to help, but that quickly felt like it would
> be a bigger project than I cared to tackle, plus I knew there would be
> a good argument that any resulting solution shouldn’t count. So I
> started as before, though I tried to take more of a zen approach this
> time vs. an OCD one. I just really took my time and let each sequence
> seep into my brain as a mini puzzle, playing with different
> preliminary move combinations and brainstorming ideas to accomplished
> multiple goals at once. This often paid off, as the extra time
> allowed me to find previously unseen shortcuts. I tried to not spend
> a lot of time at once on the puzzle (less successful near the end),
> and to not work on it if it was feeling laborious. I mostly only
> worked out one or two sequences a night, hanging out with my wife as
> she watched TV.
>
> Given the ups and downs, I figure my luck was run of the mill, so this
> is surely beatable, especially if someone happens to have more things
> "just work out" for them. Some things did work out well for me, but
> some roadblocks were frustrating.
>
> The Good:
>
> - Some preliminary move sets ended up really nice and short, which
> felt lucky.
> - It came about that I needed to do an even number of corner sequences
> (if it had been odd, I would have had to finish with a 16-move corner
> sequence instead of the 8-move sequence that must be done in pairs).
>
> The Bad:
>
> - I ended up with 1 twirled edge piece after placing the rest.
> - I was again haunted by the single flipped piece towards the end,
> though I was able to take steps to lower the cost of this. aside: I
> had initially thought this might be something that statistically
> happens 50% of the time, but now I think it may happen 75% of the
> time, since for a single unsolved piece, there is 1 possible correct
> orientation and 3 possible flipped ones.
> - I never got lucky enough to find an unintended solved piece, (which
> had happened with the first corner in my 334 length solution).
> - I seemed to have an unnaturally high number of correctly placed, but
> incorrectly oriented corners along the way.
>
> I didn’t best Remi’s effort on the face pieces, and was still only
> able to pull off 48 twists for them. The point where the edges were
> complete was blurred because I left the single twirled edge unsolved
> until near the very end, and also because I was able to place 2
> corners during my last edge sequence (I used the unsolved edge to
> my advantage after realizing it gave me some control in avoiding the
> dreaded single unsolved corner). But anyway, my last edge sequence
> was done at move 184.
>
> That’s about it I guess, without going overboard into detail…
>
> Take Care,
>
> Roice
>