   Date: Fri, 10 Dec 93 09:16:29 -0500   From: der Mouse <mouse@collatz.mcrcim.mcgill.edu >
~~~  Subject: Re: Needed: Basic elements of solving Rubic Cube:

Subject: Needed: Basic elements of solving Rubic Cube:

(Does anyone happen to know whether Ern— Rubik knows what's happened to
his name? I don't mean just here, but how common a term it's become.
And I apologize for using — instead of what I think is the proper long
accent, but Latin-1 doesn't have the proper one....)

Could you gentelmen suggest me the place where I can find the basic
(elementary) combinations to solve the cube?

There are no *the* basic combinations. I would guess there are as many
different sets of combinations as there are cube solvers.

Like the sequence to swap two "internal" side's boxes while not
changing the positions of all other "internal" boxes but probably
only rotating them?

Or could you tell me about the method to rotate some of edge elements
without swapping them?

Well, for what it's worth, when I solve a cube, I do it as follows.

(Slice turns: if I write FB, I mean turn the F-B slice in the direction
one would turn F for an F turn, similarly for other slice turns: turn
the slice as if it were carried along by the turn named by the first
letter. Thus LR and RL are inverses. Is there some standard
representation for slice turns?)

- Solve one layer ad-hoc. (This refers to a layer of cubies, not just
one face of the cube.) I often don't worry about edge flips at this
stage. Some simple operators I use:
To get corners in place: F D' F, or F' D F, depending on corner
orientation.
To get edges in place: If the cubie is on the D face,
FB/BF/RL/LR, D/D', inverse of the slice turn. If it's
on the middle layer, F/B/R/L, UD/DU, inverse of face
turn.

- Turn the cube so the solved face is L. Solve what then becomes the
R-L slice layer with a combination of R2 U2 R2 U2 R2 U2, to move
cubies around within the slice layer, and either of two sequences to
move cubies between the R layer and the slice layer:
R2 D R' B2 R2 B2 R2 B2 R' D'
FB D R' B2 R2 B2 R2 B2 R' D' BF
(The first one is a sequence that normally ends with R2, but since
the R layer is scratch at this point I often don't bother.) These
are, of course, interspersed with R, R2, and R' turns to get edges in
the correct places for them.

At this point you will have two layers solved, except possibly for some
flipped edges.

Next, corners of the "scratch" layer. Check them for placement,
ignoring orientation. They can be:
1) All in place. This is the easy case. :-)
2) Two swapped. Make one quarter-turn to reach case 3. (They
can't be diagonal, they must be adjacent - or some joker has
3) One in place, other three permuted.
4) Two pairs, each swapped. If the swaps are diagonal, turn the
layer a half-turn to reach case 1.
In case 3 or 4, the corners can be put in place by holding the cube
with the unsolved layer as U and repeating
L F L' F' L F L' F' L F L' F' twice, turning U so as to place
appropriate pairs of cubies in the UFL and UBL corners.

To orient the corners correctly, hold the cube with the unsolved layer
as F and use R B2 R' U' B2 U and its inverse U' B2 U R B2 R' with a
turn of the F face in between; this will allow you to twist the corners
into correct orientation.

All that remains at this point is positioning the edges on the last
layer, and possibly some edge flips. To position the edges, I normally
use (with U as the unsolved layer)
R2 D R' B2 R2 B2 R2 B2 R' D' R2
FB D R' B2 R2 B2 R2 B2 R' D' BF
R2 U2 R2 U2 R2 U2
with appropriate turns of U in between, swapping the FR and BR edges
repeatedly as auxiliaries while swapping pairs of edges on U to get
them in place. (The difference between the first two sequences is that
the first one swaps UB and UR, the second UB and RU.)

Edge flips are all that's left at this point. Judicious choice of
which of the two sequences above can often drastically reduce the work
to be done here, but there's often some left anyway. The basic
sequence I use for this is RL U RL U RL U RL U, which flips four edge
cubies in-place: UB, UL, DB, and DF. (A similar sequence U RL U RL U
RL U RL is similar but flips UR instead of UL; this can be thought of
as U X U', where X is the first-given sequence.) My use of this
sequence is usually ad-hoc; sequences such as X F X F' will let you
flip arbitrary pairs of edges.

Presto! You have a solved cube. :-) In practice, I often take
shortcuts; for example, if X represents the R B2 R' U' B2 U sequence,
then X B2 X B2 X B2 will twist three corners on B....

der Mouse

mouse@collatz.mcrcim.mcgill.edu     