Message #4058

Subject: Re: [MC4D] Annotated 2x2x2x2 solve.
Date: Thu, 05 Jul 2018 10:26:30 +0000

This scrambling method will always produce a solvable puzzle, and is thus valid (provided that the total number of restacking moves is always even). I’ll attempt to explain, but I’m not sure my terminology lines up with what other people will understand.

When you restack just an endcap, you are shifting the puzzle into a different kind of state. While in this state, some of the canonical moves no longer correspond to a single twist on the 4D puzzle, but after any combination of canonical moves in this state you can restack another endcap and still be in a solvable state.

In the restacked state, the 180 flip of the long face is still a valid single move on the 4D puzzle. It gives you the same effect as if you had not restacked, but instead put the long face on the inside and rotated it 180 degrees.

In the restacked state, the arbitrary juxtaposition is not necessarily a valid rotation on the 4D puzzle. If the juxtaposiiton moves the inside or outside edge to one of the long faces, that is the same as rotating that face of the cube validly, and then rotating each piece on that cube about their corner. Not something you can do in a single move on the 4D puzzle, but half the pieces will rotate clockwise and half counter clockwise, so the result will still be solvable.