Date: Thu, 29 Jul 93 08:36:14 -0400 (EDT)
From: Dan Hoey <hoey@aic.nrl.navy.mil >
Subject: Re: Hint wanted for 4x4x4

ronnie@cisco.com (Ronnie B. Kon) asks for hints for exchanging a pair
of edges:

I tend to solve using commutators, but I don't see a way here....

The key is that commutators are always odd permutations. So do the
move that is an odd permutation of the edges, then use commutators.

Dik.Winter@cwi.nl (dik t. winter) shows a neat way of moving most of
the cubies affected by the odd permutation into the top slice, where
they can be cycled using Ronnie's commutator, which cycles the
TB(R), TR(F), and TF(L) cubies:

. . 0 .
. . . .
. . . 0
. 0 . .

(I'm naming them by their edge and their near side.) I suspect Ronnie
is using something like (F Ti F') T (F Ti' F) T (F Ti F') T^2 (F Ti' F).
(For this I'm using "i" to mark inside slabs).

But you can cycle the FL(T), FR(T), RB(T) cubies directly, using a
different commutator. With more effort, there is a commutator that
doesn't mess up face centers. We are getting to the part where it's
hard to distinguish between the hintable and the obvious, but if
people send me email about not being able to figure out what
nobility is common.

My solution for the 4x4x4 always was: first corners, next edges and finally
centers. Because there are many identical pieces for the centers those are
reasonably simple. It would be much more difficult if each center had its
own place.

As I mentioned years ago, I've made places for mine by cutting corners
of to clusters of face centers and their neighboring edges on each
face.

+----+----+----+----+
|    |    |    |    |
|    |    |    |    |
+----+---( )---+----+
|    |    |    |    |
|    |    |    |    |
+---( )---+----+----+
|    |    |    |    |
|    |    |    |    |
+----+----+----+----+
|    |    |    |    |
|    |    |    |    |
+----+----+----+----+

It's not that hard to fix the face centers, just time-consuming. It's
a good thing we do the edges first, though, or it would be hard to
figure where the cuts go.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil

( So much discussion on this quiescent list will probably flush out
someone who wants to unsubscribe. Remember to send your note to
cube-lovers-request@ai.ai.mit.edu
to avoid annoyance.)