Message #3904

From: Joel Karlsson <joelkarlsson97@gmail.com>
Subject: Re: [MC4D] Solved physical 2^4
Date: Thu, 21 Dec 2017 23:27:12 +0100

Thanks Ty,

I forgot to attach the picture in my previous email so I’ll do that here
instead.

Best regards,
Joel

Den 21 dec. 2017 11:19 em skrev "Ty Jones whotyjones@gmail.com [4D_Cubing]"
<4D_Cubing@yahoogroups.com>:

Congrats!

On Thu, Dec 21, 2017 at 3:06 PM Joel Karlsson joelkarlsson97@gmail.com
[4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:

>
>
> Hello,
>
> A quick announcement, I just solved the physical 2x2x2x2. I must say
> that it’s a really interesting puzzle that’s a ton of fun to play with
> (great invention Melinda!).
>
> Regarding my solution: The first step of my solution was to get two
> colours on the "outer" (inverted octahedral) faces. I did this with
> intuition and a commutator that can be used to rotate pieces (for
> instance rotating blue->yellow->purple->blue, red->red in the attached
> picture, note that this commutator can’t be used to rotate the piece
> around any other axis so red->red is a must in the state that the cube
> in the picture is in). Since, on a 2^4, a single piece can be rotated
> in 4 different ways while the rest of the puzzle is solved, it’s
> possible to run into a parity situation during this step. This can be
> dealt with using the commutator and switching between different
> representations (which colours are on the "outer" faces).
>
> The second step of my solution was to separate these two colours on
> different faces, making half of the cube (in my case) have white and
> the other half yellow outer stickers. This can quite easily be done
> with intuition. Then, in the last step, I used two commutators (with
> some variations) to place and orient the pieces on the two faces.
>
> To switch between representations I used two restacking moves, one
> moving a cap (2x2x1) to the other side and the other splitting the
> cube into two 4x2x1 halves. This does affect the state of the puzzle a
> bit but since I only changed between representations in the early
> stages of the solution that was not a problem.
>
> The commutators I use are based on one simple idea. Isolate one or two
> pieces (depending on what you want to accomplish) from the bottom half
> on the top half (holding the cube upright), then rotate the top face
> (to accomplish a swap or rotation for example), reverse the first
> step, rotate the bottom face and lastly perform the first three steps
> in reverse. The first step can quite easily be done with 7 and 3 moves
> respectively, resulting in sequences from 7 to 32 moves (sometimes the
> first three steps are enough, depending on how much you want to
> preserve).
>
> I look forward to reading what methods others come up with and
> optimizing my own.
>
> Best regards,
> Joel Karlsson
>