# Message #486

From: Jenelle Levenstein <jenelle.levenstein@gmail.com>

Subject: 4D corner move

Date: Wed, 30 Apr 2008 14:31:48 -0500

When I am solving a 3D rubric cube I use a modification on the

layer method. The layer method involves solving one side of the cube, then

move on the next layer, until you get everything solved except the top side.

Then you need moves that can solve the pieces on the top of the cube. What I

do is I leave out one corner or edge piece in each layer. This creates a

hole that I can use to build up each layer, and later can be used to start

on the top side. When you are done with this you will have all the edges and

middles on the cube solved, and will be left with 4-5 corners. This is where

corner logic comes into play. I define a corner move as a move that

exchanges three of the same kind of pieces without messing up any other

pieces on the cube. This simplest version of this is to find a piece on the

cube that slides into place by turning one of the sides of the cube, then

take the piece out of the side, turn the bottom side so there is another

unsolved piece in the hole, then undo the moves you did to take the piece

out of the side. You will now hopefully have swapped three pieces. This same

logic will work on corners, edges, and middles.

```
When I solved the 4D cube for the first time I attempted to<br> follow something akin to the layer method I used on 3D cubes, however what I<br> ended up doing was solving two adjacent sides to start with rather than just<br> one side. I found that I could do this and still have the degree of freedom<br> required to solve the cube. I have attached a log file of me half way trough<br> solving the cube. I found I could use 3D logic in someplace on the 4D cube<br> without messing up other parts of it.
```

The question is whether corner logic will work on a 4D cube. The answer I

found was a resounding yes. First of all the first part of a corner move

where you take a piece out of its original side is a lot easier in 3

dimensions than in 4 dimensions. It is easy to take 3 or 2 pieces out of a

4D side but taking one individual piece out takes some more thought. (A 3D

corner move usually takes 7 moves but a 4D corner move takes between 12 and

18 moves) The other thing is there are more ways to mess up a 4D corner move

than a 3D one. A 3D corner piece can only be twisted three ways which means

there are only two ways to put a piece in a side incorrectly. In a 4D cube

there are many more so it is really easy to get a piece in the right side

but twisted incorrectly. Also since there are so many ways you can turn a

cube it is difficult to keep track of which three pieces you are exchanging.

I also noticed that 4D corner moves do not lend themselves to becoming

macros do to the large number of variations of moves that are possible. Even

on a 3D cube there are at least 6 different ways you can take a piece out of

a side.

My original goal of solving the 4^4 was to try to solve the parody problem

but that hasn’t happened yet.