Message #1815

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Re: God’s Number for n^3 cubes.
Date: Fri, 01 Jul 2011 19:53:46 -0500

I’d like to see results here as well, though it is a very different kind of
problem than the one Nan proposed.

Since I can’t seem to help myself from making predictions, mine here is that
things will follow what happened for the 3^3. That is, the lower/upper
bounds will get squeezed together over an extended time (the upper bound
requiring more effort) using group theory arguments, but that the group
theory arguments will run out of steam. cube20.org has a tabular history of
the 20 year saga to find God’s Number for Rubik’s Cube. Since they had to
finish off the final gap with computers, which will be impossible for the
3^4, the exact answer may literally never be known. Maybe the 2^4 will be
tractable though.

I don’t recall specific bounds being mathematically defended here before,
but I may very well have missed them or may be forgetting. Perhaps some
wiki pages for God’s Algorithm are in order to begin collating what we know.
We could have separate pages for the asymptotic and low-dimensional
problems.

Take Care,
Roice

On Fri, Jul 1, 2011 at 4:41 AM, PAUL TIMMONS <paul.timmons@btinternet.com>wrote:

>
>
> How about restricting oneself to God’s algorithm for the 3^4 case? I
> wanted to get an
> idea for the likely length of God’s algorithm (both in the QTM and the
> FTM). There must
> be some some heuristic results available now that the MC4D has been in use
> for some years now. Even more so I am interested in any results for the 2^4
> case in both metrics
> but in particular the quarter-turn one. Sorry if this information is in
> circulation elsewhere - too much information to sift through and too little
> time!
>
>