Message #3902

From: Joel Karlsson <>
Subject: Solved physical 2^4
Date: Thu, 21 Dec 2017 23:05:52 +0100


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

I look forward to reading what methods others come up with and
optimizing my own.

Best regards,
Joel Karlsson