Message #3783

From: zhulama@gmail.com
Subject: Re: One way to solve the 5-D cube
Date: Fri, 11 Aug 2017 12:18:32 +0000

OK, I just solved the 5D cube myself (3^5)! I used MC7D, and used a feature to only show cubies that I was currently solving (plus 1 and 2-color cubies)

The most important thing to understand is that the whole 5D cube has 10 faces, each face is a tesseract.
You can do 3 "normal" 3D cube moves on each face and you can also do 3 4D moves on them so the total number of possible twists on a face is 6!
What does it mean to you? Well, you can treat every 5D cube face exactly like it’s a normal 3D cube, but each of those cubes have has extra pieces inside them. You can get those extra pieces "out" by doing 4D twists.
Multi color pieces are shared between more faces so you can get those "out" by doing a 4D twist on any face that contains the piece you need!

I used the simplest step by step method that I could think of, I used the same for my 5^4 cube solution:

2-color cubies were solved by hand and a single macro to swap out cubies that were "inside"

3-color cubies
->Macros: Cycle 3 corners, Flip two corners, Twist one corner
-first solve one whole tesseract
-then solve the whole opposite tesseract
-then solve "what was left" in the middle. This took some prep-moves (F1, prep move, F2, macro, F3), but that’s amazing feature of MC7D, just like in MagicTiles!

4 color cubies

->Macros: Cycle 3 corners, Twist 2 corners, Flip 1 corner <2 and 2 colors flipped>, Flip 2 corners <only 2 colors flipped on each corner!>.
all 4 color macros were made by chaining 3 color macros (and making moves in between)
…the last macro is like a 5D move and by pure chance, I very quickly made macro for it by using old 3-color flip macro.

-first solve one whole tesseract; all algorithms were just for the outer 8 corners and then prep moves were used to "get" all the necessary pieces. After first 8 corners were solved, I did a 4D twist to put the solved ones in and unsolved out to solve those. It had to be done 4 times (Solve the outside and then 3 "rings" inside)
-then solve the whole oppisite tesseract via the same procedure
-then I realized that I can make a two 4D moves; one on any of two opposite tesseracts that were not solved yet, it was possible to solve what was left without doing any more "4D moves" and just using 4 color macros.

5D colors were perhaps the easiest because once the macros were done, I almost never had to twist the cube by hand anymore. The longest algorithm was 16624 moves (a lot of chained 4D algorithms from before)

->Macros: Swap 4 corners (two and two), Swap 3 corners, Cycle 3 corners, Twist 1 corner, Flip 1 corner inside-out
The first two macros I call "swap" because they swap outer and inner corners!
all 5 color macros were made by chaining 4 color macros (and making moves in between)

-first I used Swap 4 corners and Swap 3 corners macros to put all the "small stickers" to a correct "side" as necessary (9th and 10th color), use "Highlight by color" to show only 9th or 10th color pieces and simply swap them around until done, only needed a minute or two for this.
-then I used Cycle 3 corners to put the all the cubies in correct place
-then I used Twist 1 corner and Flip 1 corner to correctly orient each corner. The ability to do fix each corner without touching anything else made everything much, much easier.

Next step is solve 3^6.

p.s.
If I solve 3^6, where do I send the log file? MC7D site was last updated in 2013; has nobody solved 6D+ cubes since 2013 or is the site not maintained anymore?