Date: Thu, 29 Jul 93 08:59:44 -0400 (EDT)
From: Nichael Cramer <ncramer@bbn.com >
Subject: Re: Hint wanted for 4x4x4

Hi Ronnie

Let me try to restate the problem slightly to make sure we are talking

Basically, you can solve the entire cube, except that the pieces "1" and
"2" in the diagram are flipped/exchanged:

XXXX
XXXX
XXXX
X12X

Assuming this is the problem, the hint is as follows:

The problem here is that some of the face pieces are not really in their
right places. In short, one of the center slices is 1/4 turn out of phase.

The simplest way to proceed (at least for me) is to move to the following
state:

```  XX2X    (i.e. rotate one of the central slices 1/4 turn)
XXOX
XXOX
X1OX
^
|
Now, you can solve for pieces "1" and "2" and --using these pieces as a
landmark-- proceed from there.
```

Hint #2: You can help avoid this problem by solving the face pieces last.

Extra Credit: Actually, the state as shown in the first diagram above is
pretty interesting in that the analogous position on a 3X3X3 cube (i.e. a
single flipped edge cube) is of course impossible.

>From this state it is relatively easy to get to another, very interesting
state: namely the 4X4X4 appears to be completely solved except that two
opposite corners are exchanged. (Again, this is obviously impossible on
the 3X3X3.)

Left as an exercise for the reader. ;)

Nichael
ncramer@bbn.com Dr Pepper: It's not just for breakfast any more.