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Date: Thu, 10 Dec 1998 23:04:10 -0500
From: michael reid <reid@math.brown.edu>
Message-Id: <199812110404.XAA03343@cauchy.math.brown.edu>
To: cube-lovers@ai.mit.edu
Subject: fixing edge parity on 4x4x4

several people have posted maneuvers for "fixing" the edge parity
on rubik's revenge.  i haven't seen any maneuvers as short as
mine (although there might be some disagreement about "length").
recall that i am using the notation  _R_  (R underscored) to mean
turn the outer two layers together.

to switch the two UF edges:

_R2_  B2 L U2  l  U2  r'  U2  r  U2 F2  r  F2  _L'_  B2  _R2_

side effects: rotates the set of 4 U centers by 180 degrees.
also makes a 4-cycle of internal (0 faces visible) cubies.

if you're not concerned about moving centers, use

_(R2 B)_  u  _(B' D2 B)_  u'  _B_  l  _(B2 D2 R2)_

here,  _( ... )_  means the whole thing inside the parentheses
is underlined.

the maneuver that i normally use, since it's appropriate for
my solving method, is

U2  (r  U2)^5

which makes a 4-cycle of edges in the  r-slice  (and also
rotates the set of 4 U centers by 180 degrees).  this one
is short and easy to remember!

these maneuvers all work well on the 5x5x5 also.

mike