Date: Wed, 12 Jan 94 17:07:00 -0500
From: Mark Longridge <mark.longridge@canrem.com >
~~~ Subject: 4x4x4 Cube moves

Some comments on flipping a single pair of edges on the 4x4x4 cube:

```Singmaster notation on the 4x4x4 (same notation as Jeffery Adams)
--------------------------------

L left face             l inner left slice
r inner right slice     R right face
F front face            f inner front slice
b inner back slice      B back face
U up face               u inner up slice
d inner down slice      D down face
```

So L1 would be turn the left face 90 degrees clockwise and l1 would
be turn the inner left slice 90 degrees clockwise.

I'll use the suffix "2" to be for 180 degree turns and the suffix
"3" to be for 270 degree turns clockwise or 90 degree turns
counterclockwise.

This is the shortest sequence I found for flipping 2 adjacent
edges on the 4x4x4 cube (LD pair):

```(r3 D3) ^3 + (r1 D1) ^4 + Rr3 D3 R1 D1 r3 D3 R3 D1 R1 D3
```

Note the use of Rr to represent both the turns R face & r inner
slice. Counting slice turns the sequence is 25 turns, or
24 "hyper moves". This sequence moves some centre pieces around.

However, on checking David Singmaster's Cubic Circular, in issues
5 & 6, Autumn & Winter 1982 there is a shorter process on
page 15, (UB pair):

```r2 D2 l3 D1 R3 U1 R3 U3 l3 U1 R1 U3 l1 R1 D1 r2
```

This process, although more difficult to memorize, is only 16 slice
moves. It also disturbs centre pieces, although in a simpler way.
I always solve the centre pieces last on the 4x4x4.

Hope this helps!

-> Mark
Email: mark.longridge@canrem.com