Message #700

From: Klaus <>
Subject: Re: 3^4 parity problems
Date: Thu, 15 Oct 2009 21:17:55 -0000

Hi Matthew,

I will give a description of my solution when I have finished this solve and perhaps two or three other ones, depending on how close I get to Roice. I won’t explain it right now, because i don’t want anyone to break the record with my sytem until i have tried to optimize it to its limits ;-)

However, I can give a very general explanation. The method works in three steps.
In the first step I solve all of the 4c-pieces. On my first try this step took me 323 twists. After coming up with a more efficient way of solving the corners and lots of algorithms written down on paper I finally manage to solve this first step within 54 moves, despite the parity case. You gave me an algorithm to solve this parity within 22 moves and so I finished the first step in 76 moves.
The second step is solving two complete faces opposite to each other. This can be compared to solving the U and D faces on the 3^3 leaving the middle layer scrambled. In my first attempt this took me 306 moves and this step might get a real problem because I didn’t come up with a method to cut down on twists. At the moment I have done 27 twists in this step and have roughly completed about 15%.
The last step is very similar to solving a 3^3, just in a way more confusing perspective ;-) In my first solve this took me 146 twists. At that time, however, I just wanted to complete the 3^4 for the first time and didn’t watch the turn count. So I will hopefully stay below 100 turns for this step this time.

I think it should be very easy to stay below 500 turns this time, but I’m not sure if I have any chance of getting near Roice. Perhaps, if I find a way to speed up step 2 I’ll have some chance.

Have a nice twist,

— In, "matthewsheerin" <damienturtle@…> wrote:
> 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
> Matthew