Date:	  10 August 1980 2252-edt
From:	  Bernard S. Greenberg	     <Greenberg at MIT-Multics>
Subject:  Edge-cubie flipping algorithms
To:	  Davis at OFFICE-3, CUBE-LOVERS at MIT-MC

Here is my (and my apprentice :cube's) 2-edge-cubie-flipping subroutine,
which was named the "Spratt Wrench technique" after the fellow I was
talking to while cubing when I discovered it.  It is 24 quarter turns,
but is frumiously easy to perform rapidly blindfolded.

It is impossible to express it in FDRUBL (or FBURDL or FLUDBR or
whatever we're calling Singmaster-notation; let the euphony of the
acronym be the issue).  Let F be the usual, front clockwise.  Let Q
(please dont pounce on me for introducing a notation) be rotating the
floor-parallel centerslice clockwise as viewed from heaven above.

(It is clearly not IMPOSSIBLE to express it in FLURBD or BRULFD or
whatever, but it would be like analyzing a 4-voiced composition in terms
of frequencies instead of harmonies.)

Formula:    (FQ)^4(QF)^4

The sequence (FQ)^4 is called a right-handed Spratt Wrench;
(FQ^-1)^4 is a left-handed one.  Studying the effect of both of these
(which are used non-paired in other phases of my cube solution (the
sequence given above is used only during the final cadenza)) is
worthwhile; the equivalence of the formula above to ((rh wrench)(turn
the cube over)(lh wrench)), the form in which I first used it,
is due to ALAN.

The elegant formula above is best executed by a right-handed person, who
will grasp the Cube from above with his/her left hand, and use his/her
right hand to alternately turn the FRONT (which we will allow to face
right, for ease of manipulation), and the lower layer and two layers
alternately (while holding the top) to accomplish the Q moves.  This
procedure can be done with great grace and rapidity, esp.  on the Ideal
cubes.