Message #101

From: Matt Young <indigowombat@indigowombat.com>
Subject: Re: [MC4D] A new 3^4 shortest solution from a random starting state
Date: Mon, 30 Aug 2004 09:22:14 -0700

*blink blink* Yowza! That was fast. :) Guess I’ll have to take another
crack at this again now, to see if I can hold that spot long enough to get
it documented on the site. ;)

As far as avoiding single flipped pieces, or pairs of swapped pieces that
can be difficult to fix, I did hit upon a technique to avoid reaching that
situation, and used it in my last solution I submitted. It requires a heck
of a lot of planning and forethought, and really can be more trouble than
it’s worth except in this kind of competition where efficiency is what
counts, not real time spent on the solution. I can solve the puzzle much
faster in real time by just ignoring these issues and forging ahead without
so much of a plan. I’ll do my best to put together a coherent explanation
of the techniques I use and what causes this situation, but it may take a
while to figure out how to express it. I know what I do when I plan it out,
but explaining it is another matter. I’ll put some time into trying to put
it down into text that makes sense over the next couple of days.

Congratulations, Roice! Back to the hypercube I go….

–Matt Young

Roice Nelson wrote:
> I just uploaded my next entry for the ongoing shortest
> solution competition. It totaled 334 twists.
>
> I looked at Matthew’s 16 move algorithm for a bit to
> try to understand how it worked. While doing so, I
> could see there was a 4 move sequence to cycle edge
> pieces (vs. 8 in the online solution). I was really
> surprised at this, having missed it this whole time,
> and it was a cool jump in understanding of
> MagicCube4D. The downside though is this new sequence
> cycles 7 edge pieces instead of 3, so it is more
> cumbersome to use.
>
> Because this edge sequence existed, I thought for a
> while there must be an 8 move corner shuffling
> sequence out there (vs. 18 in the online solution or
> the improved 16 move sequence Matthew found). I’m not
> so sure anymore about this and if there is one, I
> haven’t found it. But based on the 4 move edge
> sequence, I did find an 8 move sequence that cycles 3
> corners and flips 2 edges. So if you use it in pairs,
> you can effectively get an 8 move corner sequence (you
> can make it so that the second use will correct the
> edges that were flipped by the first use, but all the
> while solving corner pieces).
>
> So this solution mainly takes advantage of these 2
> sequences. Face pieces I did like before, but was
> able to slightly improve my last effort. The basic
> attack of solving from the centers out (faces, then
> edges, then corners) still has never changed.
>
> At the end, I had a single flipped corner piece. This
> was unlucky when trying to create a short solution
> because it cost an additional 22 moves by itself. I
> don’t understand what causes this well enough to avoid
> it. If anyone has a good explanation, that would be
> cool. My guess is that it is similar to situations in
> the 4^3 with flipped pieces, where you can predict the
> percentage of the time they will happen, but you can’t
> realistically do anything ahead of time to avoid them.
>
> Take Care,
>
> Roice
>
>
> P.S. Here are the sequences if you are interested in
> using them (in the same notation as the online
> solution).
>
> 4 Move Edge Sequence
> Top 6 Left
> Front 5 Left
> Top 6 Right
> Front 6 Right
>
> 8 Move Corner Sequence (if used in pairs)
> Top 4 Left
> Left 15 Left
> Top 4 Right
> Right 4 Right
> Top 4 Left
> Left 15 Right
> Top 4 Right
> Right 4 Left
>
>
>
>
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