Message #699

From: matthewsheerin <>
Subject: Re: 3^4 parity problems
Date: Thu, 15 Oct 2009 17:42:34 -0000

Hi Klaus,

It would seem that you use a different method from me (not exactly surprising given the range of methods a ‘mere’ 3D cube presents) so the similarity with solving the 2^3 is maybe not exact. I believe I was in the situation where my 2^3 solve could go either way and end in parity or no parity depending on how it was solved. The corner algorithm I provided stays within the bounds of my method, which would seem to prove this.
On a 2^3 I usually opt for a method I inferred after learning the basic Human Thistlethwaite, which I think is basically Guimond (I could be wrong here). For this fewest moves challenge though I found it used too many moves, so I had to be more open-minded about things.

Out of interest on your progress, what was 50 moves?

I think you may have point about providing a scramble which cannot be reverse engineered. I agree, and I can’t think of a way to police against the trial and error approach with different scrambles either.

I suppose looking up algorithms for smaller steps would be acceptable, since methods for 3D cubes rely on learning algorithms too, which are generally found on the internet these days.

I second the request for an upper (and lower) bound for 4D, though I will stop short of asking for a God’s number, since that hasn’t been found for the 3x3x3 yet!

happy hypercubing

— In, "Klaus" <klaus.weidinger@…> wrote:
> Hi everyone,
> I also thought about this but for my system this doesn’t really make sense because it just takes to long to get to a position from where you can decide if this problem/parity occurs (Well it was only 50 turns but to optimize them took me about 3 days). I will however try to find a way to predict it earlier and to work around this awkward situation.
> But even if you decided that trial-and-error is unfair, I can’t come up with a way how to deal with that topic. Is it even possible [with the current programme] to supply a cube scrambled by hand without the possibility that someone can derive the fewest-move solution from the log-file?
> @ matthewsheerin: I have to solve some 2^3 cubes in my solution, too, and I’m using the Guimond method (if there is any faster method, please tell me). I tried to find some PLL algorithms with the computer, but I don’t think this is cheating, because if you look them up on the internet where some other people have found them by computer, or if you do the work yourself makes no difference. If you, however, compute a fewest move solution for the whole 2^3 or 3^3, I would call this cheating.
> btw: has anyone ever made an attempt to prove an upper bound for fewest move solutions on the 3^4?
> Have a nice twist,
> Klaus