# 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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