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Date: Sun, 30 Jun 1996 21:05:13 -0300
From: FERNANDO VON REICHENBACH
Message-Id: <199607010005.VAA31570@cnea.edu.ar>
To: Cube-Lovers@ai.mit.edu
Subject: Counting moves
My name is Isidro Costantini, I'm a cube lover since '81.
I used to have some cube meetings here in Buenos Aires and we have
some interesting formulas. We disserted about how to count cube moves,
and finally decided that any double move (ie: R2) are TWO moves instead
of one. This was because there are a lot of even/odd properties when
you count moves in that way. I'm quite surprised that when I checked
some pages and moves aren't count in that way. For example, to flip two
edges in it's place will always take an even number of moves (14)
(I'll put the shortest formula we have in parenthesis) (always counting
X2 as two moves) Any 3 edges xchg (12) or Flip 2 corners (14) or
Xchg 3 corners (8) is even. Any [Xchg 2 corners And Xchg 2 edges] is
always odd (ie: R1 U3 L1 U2 R3 U1 R1 U2 R3 L3 U1 = 13 counting U2 as two)
I have a collection of all the combinations of these nonFliping
corner/edges exchange ODD formulas in one face, some of them are of 17
or more movements and I wonder if there are any better than we did.
( Where's a place to check for those formulas? )
Another good example is (xchg 3 edges,noFlip) (12) R2 U1 F1 B3 R2
F3 B1 U1 R2 (9 moves using your way of counting) and another equivalent:
B3 U3 R3 U1 R1 B1 followed by F1 R1 U1 R3 U3 F3 (6+6 moves, same position)
Another way of counting could be adding the suffix (1,2 or 3) (counting
only clockwise moves) which would preserve parity as well.
I would be pleased if some one can tell me about this subject.