Message #895

From: matthewsheerin <>
Subject: Re: [MC4D] Sub-1000 for 4^4
Date: Mon, 07 Jun 2010 23:53:59 -0000

Andrey, that makes you sub-1000 for 4^4 and sub-2000 for 5^4, an impressive set of records!

It will be interesting to see new methods developed here specifically designed for 4D hypercubes, and how efficient they can be made to be. It has crossed my mind that one of the methods used by computers to solve efficiently is the Thistlethwaite algorithm, which has been adapted slightly for humans (Ryan Heise has a tutorial if you don’t know it). I wonder what move counts could be achieved applying it to 4D, though since the last section of the solve relies on half-turns the current MC4D interface isn’t ideal for it. If 180 degree face turns only counted as one move, then the method could be interesting, though probably very difficult to apply in 4D. Also, does anyone have any idea what God’s number is for any 4D cubes? Since it hasn’t been pinned down for the 3x3x3, I doubt it will be known any time soon!

I am currently working on fine-tuning my 3^4 method, and will be revisiting the 4^4 and 5^4 when I have finished that. Hopefully Melinda is correct: like Remi I’m interested in speedcubing so hopefully that will help a little (I wonder how many speedcubers we have here?).

Now that Andrey has taken on the 4D cubes so dramatically, I have a feeling that several people (Roice, Remi, I’m looking at you here) will be having another go at the top spots, and we may get some records changing hands some more. Could be exciting!

Well done Andrey, keep up the good work!


P.S. Remi mentioned different ‘steering’ for the 2^4 in the new MC4D, did I miss something?

— In, Melinda Green <melinda@…> wrote:
> Yes, you are right that we are far from god’s algorithm and perhaps we
> always will be. You are also right that this is because the solutions we
> use are designed specifically for human use. I did not mean to suggest
> that we are getting close to the limits of what is possible; just that
> it feels as if we’re beginning to feel the limits of these particular
> methods. Will we be able to find new, more powerful methods that humans
> can still apply? This is a very interesting question though I doubt that
> dimensionality has much to do with it.
> The July 2008 issue of Scientific American contained an article with a
> lovely sidebar titled "Puzzle Tactics" that teaches you how to find a
> solution to any twisty puzzle.
> (
> It clarified the way that all these solutions are generated and helped
> me master the Megaminx.
> Assuming it is true that everyone uses the same high-level approach to
> generate solution methods to any twisty puzzle, the real open question
> in my mind is whether there are any *other* approaches that can result
> in more efficient solution methods. I expect the best wisdom in this
> area will be found in the speed-cubing community since they are all
> about efficiency. Remi, I think of you as the representative of that
> community. What do you think?
> -Melinda
> Andrey wrote:
> > Melinda, Remi, thank you!
> > I haven’t try 2^4 yet. But it seems to be much more 4D than large cubes - so it will be interesting to do something with it )))
> > As for real difficulties of n^4, I think that we are very far from it. All human algorithms are based on some restricitions of possible actions - so we are closing short ways and select long but predictable. I tried to close as few ways as possible - but to have small enough set of resulting positions. I’m sure that there better ways (that use full power of 4D geometry)