Message #1762

From: Eduard <baumann@mcnet.ch>
Subject: Re: Notes on 3^4 alt, 2x2x3x3 and 2x3x4x5
Date: Wed, 08 Jun 2011 07:56:19 -0000

Hi Nan,

Your notes are very interesting! Thanks a lot!

— In 4D_Cubing@yahoogroups.com, "schuma" <mananself@…> wrote:
>
> Hi everyone,
>
> In the last three days I solved 3^4 alt, 2x2x3x3 and 2x3x4x5 on MPUlt. Actually before that I tried the 120-cell on MPUlt. After spending 3 hours on it, I decided I was not patient enough to do it. So I switched to small puzzles. The common property that three puzzles share is that they are all "subgroups" of tesseract puzzles. However, I have quite different experience solving them.
>
> ————
> 1. 3^4 alt (turning around 2C by 180 deg and 4C by 120 deg)
>
> When I first thought of this puzzle, I was imagining the 180-deg-only Rubik’s Cube. Please try to scramble and solve a Rubik’s Cube using only 180 deg turns. It’s pretty simple and very different from the common Rubik’s Cube. 3^4 alt, however, is not that different from 3^4.
>
> 2C pieces behave in the same way as in 3^4, except odd permutations are forbidden. Flipping two 2C’s is possible.
>
> Two 3C pieces can be rotated simultaneously (the permutation of stickers of each piece is a 3-cycle), but not flipped ((a,b,c)->(b,a,c) is impossible) in place. Note that in 3^4 the latter thing is possible.
>
> 4C vertices belong to two orbits. Before solving it I only prepared the algorithms for rotating two 4C pieces in the same orbit (the permutation of the stickers on each 4C is a 3-cycle). But I met the situation that I needed to rotate two 4C in different orbits. It was a surprise and I had to re-solve a large fraction of the puzzle.
>
> Overall, 3^4 alt is quite similar to 3^4.
>
> ————-
> 2. 2x2x3x3 (turning around square by 90 deg and rectangles by 180 deg)
>
> This puzzle is similar to the duoprisms in MC4D. The cells are of two kinds: 2x3x3 cells and 2x2x3 cells. Stickers in one type of cells never visit the other type of cells. The above properties are shared with all the duoprisms.
>
> Compared with the duoprims in MC4D, 2x2x3x3 is a really small puzzle. Once the algorithms are ready, it doesn’t take long at all to solve it.
>
> ———-
> 3. 2x3x4x5 (180-deg only)
>
> This puzzle is truly similar to the 180-deg only 3D puzzles: each sticker can only stay in the original cell or the antipodal cell.
>
> The direct analog in 3D should be 2x3x4 and 3x4x5. I have solved 2x3x4 and 3x4x5 on a simulator. So I pulled out my notes for them. What I found was pretty vague, like, "use algorithms like [R,u]x3 cleverly". I don’t have a systematic analysis for this kind of puzzle. Usually I just try my best to solve one or two pieces, and sometimes magically the others fall into the correct slots. It seems like many pieces are strongly correlated. But I don’t understand the relation between pieces. Sometimes I solve centers first and sometimes corners first.
>
> So I had to boldly go to 2x3x4x5 and hoped magic happened again. I was not that lucky.
>
> It took me a long long time to solve it. The method was again very heuristic. At the end I was solving 3C pieces. Once I saw a situation, I had to look for algorithms ad hoc. Application of macros is limited in this puzzle, because a macro recorded on a, say, 2x3x4 cell cannot be used on a 2x3x5 cell. So I alternated between a testing log file and a solving log file several times.
>
> To give you an idea how frustrated I was, let me tell you this: just now I tried to revisit 2x3x4x5. But after two minutes I was lost again. I didn’t know what to do, because I’ve never found a systematic solution.
> ——–
>
> This is my story of solving the three "subgroups" of the cube. 3^4 alt is very similar to 3^4; 2x2x3x3 is basically a duoprism; 2x3x4x5 is solved heuristically, with pain.
>
> Nan
>