3^3 but with 3^4 characteristics

[Blobinati Cuber]

Hello everyone! Recently I began thinking about making a 3x3x3 cube with some 3x3x3x3 hypercube moves allowed. This happened when I started my journey into the world of 2D puzzles. I thought about how the moves on the 3^2 are actually just mirroring a side. So if we applied this type of mirroring move to the 3^3 then that could make the puzzle more interesting and increase the total number of states because it would allow the colour scheme to be changed for certain pieces. 

Another type of move (that Melinda introduced me to) is found on the n-dimensional face turning puzzle wikipedia page and is a flipping move. That is like physically taking off a layer of a cube and flipping it so that the pieces that used to touch the core are now on the outside.

Using these moves, I wonder how much harder the normal Rubik's Cube would be! Let me know if anyone has any thoughts on this, or maybe a calculation of the number of states, or anything else :)

[Nan Ma]

Hi Blobinati,

Many years ago I did implement some cubes based on reflection (mirroring) moves in a webpage. You can play here:

http://nan.ma/reflecube/index.html

There are several variations one can try. Try and tell us how hard they are!

Nan

Sent from my iPhone

On Apr 20, 2021, at 7:30 PM, Blobinati Cuber <rowan....@gmail.com> wrote:

Hello everyone! Recently I began thinking about making a 3x3x3 cube with some 3x3x3x3 hypercube moves allowed. This happened when I started my journey into the world of 2D puzzles. I thought about how the moves on the 3^2 are actually just mirroring a side. So if we applied this type of mirroring move to the 3^3 then that could make the puzzle more interesting and increase the total number of states because it would allow the colour scheme to be changed for certain pieces. 

Another type of move (that Melinda introduced me to) is found on the n-dimensional face turning puzzle wikipedia page and is a flipping move. That is like physically taking off a layer of a cube and flipping it so that the pieces that used to touch the core are now on the outside.

Using these moves, I wonder how much harder the normal Rubik's Cube would be! Let me know if anyone has any thoughts on this, or maybe a calculation of the number of states, or anything else :)

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[Melinda Green]

Dear Nan,

Thanks for the link! You did a great job on that puzzle, just like with all other puzzles.

I'll just add that Andrey's Magic Puzzle Ultimate also supports a variety of mirror moves. See attached screen shot. Mirror-Z is the case I like best where it doesn't matter which sticker you click; the whole 3D face inverts itself through it's center. Please check it out. For all the new folks here, Andrey was a giant. (No, not André the Giant.) The best way to honor him is to use his incredible software.

-Melinda

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