Message #100
From: Roice Nelson <roice@gravitation3d.com>
Subject: A new 3^4 shortest solution from a random starting state
Date: Sun, 29 Aug 2004 10:46:21 -0700
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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