Message #896

From: Andrey <andreyastrelin@yahoo.com>
Subject: Re: [MC4D] Sub-1000 for 4^4
Date: Tue, 08 Jun 2010 04:00:41 -0000

I use my own version of Thistlethwaite’s-like algorithm for 3^3. Actually, I know only the common idea of the original version, so all stages were developed from the begining. Sequence of operations for 3^3 looks like this:
1) orientation of edges
[single-turns of 2 faces are forbidden]
2a) orientation of corners
2b) first rearrangement of edges
[single-turns of 4 faces are forbidden]
3a) first rearrangement of corners
3b) second rearrangement of corners (alignment of tetrahedrons)
3c) second rearrangement of edges
[all single-turns are forbidden or enabled in some "operations"]
4a) third rearrangement of corners (usually it’s 1-2 twists)
4b) third rearrangement of edges
[all turns of two faces are forbidden, cube is reduced to 3^2]
5) final stage - not more than 8 turns

You can see how it works in my log files - last stages of all three 4D cubes are 3^3. Yes, it’s not very efficient with its double-twists (but I can take back something by usage of middle layers - that is counted as 2 turns in classic algorithm).
I tried to develop something like that for 3^4. First stages were beautiful - to limit twists of 4 sides to D4 (group of 4-prism) and orient 2C cubies, then limit all sides to D4 (reduce cube to puzzle of two tori), but then… Looks like I need to solve more puzzles to find proper operations for them. When I counted steps for some way of solving, I got much more than 300 and decided to find another way of group reduction.
God’s number for 3^4 is more than 55 (log(N)/log(23*7)), and I think that is around 60-70.

Good luck!
Andrey