Message #798

From: Roice Nelson <>
Subject: Re: [MC4D] Records: Now with moar images!
Date: Wed, 25 Nov 2009 12:20:56 -0600

Great stuff Chris!

Your block solution approach is interesting.

I also like your notations thoughts. One tiny observation I had was that
there is redundancy in it, so for example 3c(5,5,4) could be reduced to
(5,5,4), or even simply 554 for that matter. In any case, I definitely like
your approach to distinguish between the various kinds of piece types, since
number of colors is not discriminating enough.

There are some other situations that might be relevant to these piece
labeling thoughts. As just one of many examples, there are two types of 4C
pieces on the length-3 simplex (one with 4 tetrahedral stickers and one with
4 octahedral stickers), and again number of colors falls short for
classification. Unfortunately, this time both piece types are connected the
same number and types of faces. I’m not sure how one might be able to
elegantly distinguish those via notation. Maybe sticker shape has to come
into play or something…

Take Care,

On Wed, Nov 25, 2009 at 10:07 AM, Chris Locke <>wrote:

> Hello everyone!
> I would’ve sent an email off after finishing the length 5 {5}x{4} duoprism,
> but it was like 3am my time, so I chose sleep over email. I hope you can
> all understand ^^
> First, I was asked to give an update on how my solution to the length 2
> {6}x{6} duoprism, especially since the program now has the ability to do all
> possible twists of these length 2 puzzles, so there are some more
> complications that can arise. The main thing I noticed was that you now
> need to keep track of the relative orientation of the colors of each torus.
> If you put the 2c pieces into place without considering this and you get it
> reversed, then you won’t be able to solve. I carelessly neglected this, and
> ended up chosing the wrong orientation along the way. I was too lazy to
> restart and just fixed the problem there. Luckily it wasn’t too hard to
> just flip the colors of one torus, and then fix the damage. Saved me time,
> but not twists :P
> Now, the big one is the length 5 duoprism {5}x{4}. I totally didn’t expect
> to attempt this puzzle, but I was playing around a bit after solving the
> {6}x{6} 2, and got toying with the length 5 puzzles, and decided to see if I
> am able to fix some 1c centers in them. This quickly turned into a a desire
> to go for a full solve. When picking which to do, I settled on the {5}x{4}
> over the {5}x{5}. While it’s true that the {5}x{5} has less move sequences
> you need to learn because the two torii are the same shape, the pentagonal
> shaped toruses always seem more awkward to work with. Basically, I felt
> more comfortable working with the nice cube shaped faces :P. My adversion
> to the pentagonal torii seemed to be justified a little though. I had a bit
> more trouble finding macros for fixing the centers, faces, and edges of the
> pentagonal torus.
> By the way, one notational convention I used in my notes and macro names is
> the following. We all know and use 1c, 2c, 3c… to describe pieces. In
> these duoprisms though, I pointed out previously, there are different kinds
> of pieces depending on their locations. For instance, among 2c pieces in
> the {5}x{4}, there are 2c pieces between two pentagonal facets, 2c pieces
> between a pentagonal and square facet, and 2c pieces between two square
> facets (facet is just the term for a hyperface - so in 4D that is a 3D
> hyperface which are the ‘faces’ you twist). I label these different pieces
> 2c(5,5), 2c(5,4), 2c(4,4). Similarly you can have 1c(5), 1c(4), 3c(5,5,4),
> 3c(5,4,4).
> Because I felt less comfortable with the pentagonal facets, I always made
> an effort to fix those blocks first (I also distinguish between ‘fixing’
> pieces as putting the blocks together, and solving them by putting them in
> the correct relative location). I was able to fix all the 1c pieces without
> any macros thankfully. Then, I worked my way from there, and developed
> macros along the way for each of the kinds of blocks present that needed
> fixing. One thing that is nice about fixing blocks over placing them, is
> that you can freely rotate the blocks into any arbitrary position you want
> before applying a macro, and since you aren’t yet solving them, you don’t
> need to be careful about undoing the sequence afterwards (conjugation).
> This meant that I was able to use my 3swap algorithms to almost invariably
> place 2 pieces in the correct block and orientation. When I got to actually
> solving though, sometimes the move sequences to put everything in place to
> solve 2 pieces is too long to remember how to undo, so I usually settled for
> less moves to get one piece in, and as such could cut down that part of the
> solve a fair bit.
> Oh yeah, I also ran into a problem I had before with the solution to the
> reduced {5}x{4} 3 puzzle. In this length 3 puzzle, you can have a case
> where you think all your 2c pieces are placed nicely, then end up with a
> case where you have to swap just two 2c pieces, which seems at first to be
> an impossibility. I found out how to fix this before, and again since I
> didn’t remember how I fixed it, had to come up with it again, by examining
> the effects of each kind of twist. By looking at all the twists, and
> determining whether it is an even or odd permutation of 2c pieces, you can
> find that by doing a single twist of a square facet, you are doing a 4cycle
> of 2c(5,4) pieces, which is odd. So you can basically fix this problem by
> using your 3swap algorithm to rotate the 2c(5,4) pieces a quarter-turn, then
> you will be left in a case that is more directly solvable. This same
> problem can arise in any case where there are odd permutation twists
> (therefore, it can also happen in the hexagonal duoprisms).
> Anyway, this last step of solving I was able to do actually in less then
> half the moves of my first time solving the {5}x{4} 3 due to being more
> comfortable with these newer puzzles now. It was quite a marathon of
> working a fair bit every night for 3 nights, but it’s over now and was worth
> it. I’m actually now able to solve my 5^3 cube without having to resort to
> any memorized algorithms now because of my experiences with this and other
> puzzles. Very cool.
> It’s late here again, so I’ll finish with that. The biggest advice I can
> give is that while these bigger puzzles seem intimidating, if you have
> patience and some experience with other bigger puzzles (like 4^4 and 5^4)
> then even these monsters are conquerable!
> Chris
> 2009/11/25 Melinda Green <>
>> Dear Cubists,
>> I had been thinking that we really needed to sex-up the records and puzzle
>> pages with images, so I took some screen shots of the {5}x{4} in several
>> lengths, uploaded them to the wiki, and inserted the appropriate one into
>> each length section of the {5}x{4} puzzle page<>and one example into the records
>> page <>. I think that this
>> turned out quite well and would like to propose that we do this in general.
>> I would be very grateful if someone would do this for the rest of the
>> puzzles. This would be a great way for a non-programmer/non-solver to make a
>> valuable contribution to this project. I’ll be happy to offer suggestions on
>> how to capture, edit, upload, and format images if anyone has questions.
>> In related news, notice that the {5}x{4} records now includes the first
>> length-5 solution by Christopher Locke<>.
>> Well done Christopher!!
>> -Melinda