Message #419

From: Roice Nelson <roice@gravitation3d.com>
Subject: tag, you’re it!
Date: Sat, 08 Sep 2007 18:52:22 -0500

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

1. 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