Date: Wed, 31 Mar 82 22:26:00 -0500 (EST)
From: David C. Plummer <DCP@MIT-MC >
~~~ Subject: 4**3,5**3

NO, NO, NO !!!! You CANNOT treat 1 of the center slices of a
4x4x4 as a center of a 3x3x3. Suppose you did this for one axis,
and for the other two axes you treated both "centers" as a unit
(and therefore the center slice of a 3x3x3). Now take one of the
axes with a double width center, and rotate an outer slice 180
degrees. Suppose the front face looked like this:

```+####+####+####+####+
#    #    #    |    #
#    #    #    |    #
+####+####+####+####+
#    #    #    |    #
#    #    #    |    #
+----+----+----+----+
#    #    #    |    #
#    #    #    |    #
+####+####+####+####+
#    #    #    |    #
#    #    #    |    #
+####+####+####+####+
```

You rotate the top slice and the front face now looks like:

```+####+####+####+####+
#    |    #    #    #
#    |    #    #    #
+####+####+####+####+
#    #    #    |    #
#    #    #    |    #
+----+----+----+----+
#    #    #    |    #
#    #    #    |    #
+####+####+####+####+
#    #    #    |    #
#    #    #    |    #
+####+####+####+####+
```

Notice that the top layer does not go very well with the bottom 3
layers. The 5x5x5 has similar problems.

I think the right way to solve both the 4x4x4 and 5x5x5 at first
is to use mono-flips. Once conceptually understood, they are
very powerful and easy to visualize.