# Message #702

From: matthewsheerin <damienturtle@hotmail.co.uk>

Subject: Re: 3^4 parity problems

Date: Fri, 16 Oct 2009 15:33:27 -0000

Hello again,

This has certainly turned out to be an interesting discussion!

That’s an interesting method you have there Klaus, and I’m sure I’m not the only one here who would like to see how far it can be pushed. I have been considering various ideas for reducing move counts, which I think would be hard to explain, and are also unproven just now. Despite the fact I want to with all this talk, I will not be attempting any fewest moves solves any time soon. I have my reasons, not least of which is a lack of free time now I have started uni. I will eventually return to the idea, especially since your 54 move solution for the corners, had it not encountered parity, would have been able to demolish the current record for the 2^4, and I think it would be worth your while considering having a crack at that one. I can think of how to significantly reduce my move count for the 2^4 and the 3^4, but the question of whether my ideas work and by how much will have to wait.

@Melinda: I would consider using a computer generated solution to certainly be cheating, even if the person in question wrote the program. I have no qualms about using macros created by the solver (though I slowly stopped using them for my 4D solves, I feel they hinder the move count), but the thinking behind the solution should be all, or at least mainly, done by a human.

Just to finish, I am looking forward to new 4D puzzles becoming available. I have considered it a possibility from the start and I am excited to see what they look like and how they behave. Many thanks to the wonderful people helping to bring them to life! :)

happy hypercubing

Matthew

— In 4D_Cubing@yahoogroups.com, "Klaus" <klaus.weidinger@…> wrote:

>

> 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,

> Klaus

>

> — In 4D_Cubing@yahoogroups.com, "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

>