Almathera Ten Pack 3: CDPD 3/Almathera Ten on Ten - Disc 3: CDPD3.iso/fish/726-750/733/cube/cube.tutor

Text File | 1995-03-18 | 19KB | 431 lines

              TUTORIAL FOR SOLVING RUBIK'S CUBE
            (C) Copyright 1991 by Martin Gitelson
                  Shareware
---------------------------------------------------------------------------

            CONSTRUCTION AND NOMENCLATURE

---------------------------------------------------------------------------

   The cube was invented by Erno Rubik, a Hungarian teacher of architecture
and design.  It consists of 27 "cubelettes" arranged in 3 by 3 by 3 order.
Each layer is capable of being turned with respect to the other two.  The
pieces are not independent and must be moved in groups.  They behave like
quarks.  One piece cannot be twisted without twisting another.

   It is not a true cube in the sense that it is a stack of smaller cubes.
In the first place, you can never see the center cubelette.  It is
constructed similarly to a little girl's jack with three axes like the xyz
axes of solid geometry.

   The first type of cubelette is the face or center piece.  It has only one
color.    If one center piece happens to be colored red and the opposite side
is colored orange, then they will always stay on opposite sides from each
other no matter how you turn the various layers.  There are 6 center pieces.

   The second type of cubelette is called an edge piece.  It has two colors.
It may occupy only edge cubicles, never a corner or center spot.  It can be
twisted so it's colors appear reversed, but only if another one is twisted
along with it.    There are 12 edge pieces.

  The third type is the corner piece.  They have three colors.    There are 8
of them.  Just like the edge pieces, they are restricted in their movements.
A corner piece can be in a particular corner in any of three orientations.
If you twist one clockwise, you must either twist a second one counter-
clockwise or you must twist 3 clockwise.

   Each edge cubelette can also be called by two-letter names, like uf for
upper-front ur, fd, etc. indicating it is part of each named side.  The
corners cubelettes can have three-letter names like ufr meaning they have
faces located on the three named sides.  The center cubelettes can only
have one letter names.

   The sides are labeled Up, Down, Left, Right, Front and Back because back
and bottom have the same initial as do right and rear.    Front is the side
that happens to be facing you.    Right is on your right.

   A cubelette is the colored piece, and a cubicle is an area of space into
which a cubelette can move.

   When turning a side, my nomenclature is not the same as everyone else's
because I'm lazy and don't like to keep hitting the [ENTER].  Instead of
calling a counterclockwise/anticlockwise turn "r-1 [ENTER]", I just call it
"ar" because by the time you hit the minus key, the right side has already
turned clockwise.  My program uses r,ar,2r,l,al,2l,f,2f,af,b,ab,2b,u,au,2u,
d,ad,2d to indicate turning a side or layer.

   When turning a side, u means clockwise and au means anticlockwise looking
from OUTSIDE toward the center of the cube.  Remember when turning the back
side that when looking at the back of a clock it appears to turn backwards.

   A process is a series of moves designed to to a certain job.
lar-f-ral-2u-lar-f-ral is one of my favorites.    It moves three edge pieces.
I like it because it is easy to remember, though inefficient; but with
variations it can move the same three edges any way you want.  It is
composed mostly of rals and lars.

   My nomenclature for orienting the cube is also different.  Orient right
means moving the front of the cube where the right side formerly was.  It
just seems to make more sense to me, because you see the picture move to the
right.    The options are ol, or, ou, od, oc, oa    the last two for orient
clockwise and orient anticlockwise because counterclockwise has the same
initial as clockwise.

-----------------------------------------------------------------------------

        SHORT COURSE OF INSTRUCTIONS FOR SOLVING

-----------------------------------------------------------------------------

   If this is your first encounter with Rubik's cube, I suggest you first
experiment with it to see how the pieces move.    Most people can get the
first layer without any instructions.  Try at least to get the first four
edge pieces in place.

   You might also like to run the program in slow motion letting it solve
the cube for you.  Pull down the Palette menu and with the mouse pick up
colors and paint the cube on the screen to exactly match your scrambled cube.
Once you have it painted on all six sides, hit the "1" key for single step.
Then hit [RIGHT AMIGA][s] to solve it.    The program will make one move at a
time, giving you a chance to follow along and fix your cube.  Hit any key to
see the next move.

   My method of solution consists of 7 parts.  This is the solution you will
find by hitting the AMIGA S.  You can solve in about 60 to 110 turns using
this method.  These must be done in the proper order.  Doing VI, for
example, will mess up VII.

       I)  Put the four upper edge pieces in place, one by one.
      II)  Put the four upper corners in place, one by one.
     III)  Turn the cube over so the upper side becomes the lower and put
       each of the four middle layer pieces in place.
      IV)  Place the last four corners in their proper places ignoring the
       way they may be twisted.
       V)  Twist them, if necessary.
      VI)  Place the last four edges ignoring their twist. (actually, the
       program will try to twist them most of the time, if the processes
       are available.  You can do it this way if you have a good memory.)
     VII)  Twist them, if necessary.


   I) Upper edges  *********************************************************

   Select a color to call the upper surface and another one to call the
front.    My favorites are white for the upper and red for the front.

   Find the edge piece which is red on one side and white on the other and
move it into it's correct spot.  Do the same for each upper edge piece in
turn.  It shouldn't take more than 4 or 6 turns per piece.  Usually one or
two will do it.  Sometimes you may have to temporarily move a piece that has
already been placed.  Just be sure to move it right back.

   After you get the four edges in place---make sure the colors match up on
all four sides, we can go to the upper corners.  The corners are harder to do
but easier to explain.

   II) Upper corners *******************************************************

   Look over the lower layer to find a corner piece that needs to go into
the upper layer.  Remember to check all three colors to find the right one.
It can be facing in any of three directions while in the bottom.  The white
colored side or upper colored side can be pointing either down, left or
right.    Try to find one pointing left or right because they only take three
moves while the ones pointing down take six.

   After you find one, turn the down/bottom layer so the chosen cubelette is
directly underneath the target cubicle.  Since most people are right handed,
let's make sure the chosen cubelette and the target cubicle are on the right
front side.

   If the upper colored surface is pointing right do the next 3 steps:

   1)  Turn the right side anticlockwise 1/4 turn.     ---------------- ar
   2)  Turn the down side to bring the chosen cubelette again directly
       underneath the target cubicle.       ---------------------------- ad
   3)  Restore the side you just turned in step 1.   ------------------- r

   If the surface colored like the upper side is pointing left (actually, it
will be pointing directly at you), do the next three steps:

   1) Turn the front side clockwise 1/4 turn.       --------------------- f
   2) Turn the down side clockwise 1/4 turn.       --------------------- d
   3) Restore the front side.               -------------------- af

   If the upper colored surface is pointing down, do the following six
steps:

   1) Turn the right side anticlockwise 1/4 turn. -------- ar
   2) Turn the down side clockwise 1/4 turn.      --------- d
   3) Restore the right side.              --------- r
   4) Turn the front clockwise.           --------- f
   5) Turn the down side 1/2 turn.          -------- 2d
   6) Restore the front side.              -------- af

   If the chosen piece is in the upper layer, you will first have to move it
down by using any of the three above processes.

   You must do each corner one at a time.  If you discover that you have
misplaced an edge, forget about the corners until you get the edges back in
place.    It is much easier to do the edges first.

   III) Middle layer ******************************************************

   Once the upper layer is perfect, turn the cube upside down and forget
about it.  Not completely; you want to check once in a while to insure
hasn't become out of place.

   For now, it is easier to move an edge piece down from the upper layer
to the middle layer rather than sideways from another middle layer spot.

   Look around the upper layer (which used to be the down layer) for an edge
to move down.  Once you find one, match the color next to the color of a
center piece.  Hold the cube so the piece in question is facing you.  You
should see at least 5 pieces of all one color making an inverted T.  The
edge piece will want to go either to your left and down into its proper
position or right and down depending on how it happens to be twisted.

   If it wants to go right and down apply the following process:

       urauarauafuf         You must memorize this process.

   If it wants to go left and down apply the mirror image process:

      aualulufauaf         You must also memorize this one.

   If you cannot find the piece in the upper layer, or if it is in it's
correct position but twisted, it is easier just to move it back up using one
of the above two processes and then move it back down again.  Twisting it
takes 14 moves anyhow.

    Notice the similarity of the two processes.  Once you memorize one, the
other is just the reverse.  Notice also what you are doing.  You are
bringing up a corner piece that has already been placed, matching it up with
an adjacent edge piece and then moving the two together back down into
position.  Sometimes it's easier to remember what to do than memorizing a
series of moves.

    IV) Final layer---place corners ***************************************

    Now we are going to check and see if the corners are in the correct
order.    Find two adjacent corner pieces that have a common color other than
the top color which should now be yellow or blue depending on how your
particular cube is colored.  Disregard the fact that they might be twisted.
Turn the top layer until these two pieces are on the correct side.  If you
selected two adjacent pieces colored orange, for example, move both of them
to the orange side.  If you can't find two adjacent orange, look for two
adjacent green or whatever you can find.  Now check the other two corners.
You will find one of three conditions:

   1) All the corner pieces are in their correct corners.
   2) Two adjacent corner pieces must be switched.
   3) None of them are in the correct place.  This means that two diagonals
      must be switched.  If you give the up layer 1/4 turn you can see this.

      back
       ----------           ----------        ----------  ^
       |ok|  |ok|           |ok|  |ok|        |ok|  |  |  |
       ----------           ----------        ----------  |
 left  |  |  |    |  right       |  |  |    |        |  |  |  |  |
       ----------           ----------        ----------  |
       |ok|  |ok|           |  |  |    |        |  |  |ok|  |
       ----------           ----------        ----------  |
     front               <-switch->        <--switch---

    To switch two adjacent pieces, hold the cube like in the picture and use
this string:

    ruaraf-au-frauar-2u        (bauafuabauf-2u  is shorter.)

    To switch two diagonal pieces, hold the cube any way (as long as the
top side remains the top) and do:

    ruaraf-2u-frauar-( u, 2u, or au as necessary )

    ufurauaraf is shorter but harder to remember.

   The longer strings are easier to remember because they are the same
except for the middle turn---either au for adjacent or 2u for diagonal.
(Guess what "u" would do.)

    V)    Final layer---twist corners ***************************************

    Now, you will find one of seven patterns of twists.  Pick out the
correct  picture, hold the cube as in the picture and apply the process
given in the picture.  Some patterns need two processes.  The x's show the
location of the top color.  (If your pattern is not here, someone must have
taken your cube apart and put it back together wrong.)

    It's not as complicated as it looks at first glance.  I only use three
strings.  The second one is the reverse of the first; and the third one has
an extra clockwise zig in the middle of a bunch of counterclockwise zags.
You don't need the third string at all.  You don't need the second one either
if you hold the cube the right way and use the first one three times.

    The secret is remembering how to hold the cube.  For all but picture 2,
start out using string 1; then see what needs to be done from there.

    These processes are like all the other processes.  If you stand there
and do them enough times, you will eventually end up where you started from.
These have a cycle time of three if you end up with 2u.  The cycle time is
six if you don't.
                      |
          xx      PICTURE 1       |     xx          PICTURE 2
       ----------              |    ----------
       |xx|  |    |              |    |  |  |  |xx
       ----------              |    ----------
       |  |  |    |  araurauar2ur-2u    |    |  |  |  |  ar2uruarur-2u
       ----------              |    ----------
       |  |  |    |xx              |  xx|  |  |xx|
       ----------              |    ----------
    xx                  |
-----------------------------------------------------------------------------
                      |
          xx      PICTURE 3       |           PICTURE 4
       ----------              |    ----------
     xx|  |  |    |  araurauar2ur-2u    |  xx|  |  |  |xx
       ----------    Picture 1          |    ----------
       |  |  |    |    then: orient     |    |  |  |  |  araurauarurauar2ur
       ----------  araurauar2ur-2u    |    ----------
     xx|  |  |    |    Picture 1 again  |  xx|  |  |  |xx
       ----------              |    ----------
          xx              |
-----------------------------------------------------------------------------
                      |
    xx          PICTURE 5       |     xx      xx      PICTURE 6
       ----------              |    ----------
       |  |  |xx|   araurauar2ur-2u   |    |  |  |  |    araurauar2ur-2u
       ----------     Picture 1       |    ----------      Picture 1
       |  |  |    |     then: orient r  |    |  |  |  |      then: orient l
       ----------   ar2uruarur-2u     |    ----------    ar2uruarur-2u
       |  |  |xx|     Picture 2       |    |xx|  |xx|      Picture 2
       ----------              |    ----------
    xx                  |
-----------------------------------------------------------------------------

    xx           PICTURE 7
       ----------
       |  |  |xx|    araurauar2ur-2u
       ----------      Picture 1
       |  |  |    |      then:
       ----------    ar2uruarur-2u
       |xx|  |    |xx    Picture 2
       ----------
-----------------------------------------------------------------------------

    VI) Final layer  place edges *******************************************

    There are four patterns into which the last four edges fall.

       1) Swap opposites.  (Swap two pairs of opposites---4 pieces)
       2) Swap adjacents.  (Swap two pairs of adjacents---4 pieces)
       3) One is in place and the others need to be cycled clockwise.
       4) One is in place and the others need to be cycled counterclockwise.

    For swapping opposites, hold the cube in any orientation and the best
string I have is:

    rl2uaralafab2ufb

    For swapping two adjacents, hold the cube so the ones you want to swap
are on the upper-front and upper-right side:

    2f2bad2l2f2b2r2f2bd2f2b

(You also swap the upper-left and upper-back at the same time, naturally.
Maybe naturally doesn't fit yet.  You can never swap only two edges.  You
can swap four or cycle three; or you can swap two edges and two corners.
The strings we used to swap the two corners in step IV also swapped two
edges; but I didn't mention it at the time.)

    To cycle three pieces in the clockwise direction, hold the cube so the
good piece (doesn't need to move) is on the upper-left and use:

    2rufab2rafbu2r

    Counterclockwise is the reverse.  Hold the cube so the good piece is on
the upper-left:

    2raufab2rafbau2r

    VII)  Final layer  Twist last four edges *********************************

    As with all the others, more than one pattern is possible.    Here we can
have three.  If you have an odd number of pieces twisted, then somebody took
your cube apart and put it back together wrong.  You can't tell until you
get all the way down here.

    1)    Two adjacents are twisted.
    2)    Two opposites are twisted.
    3)    All four are twisted.

    For two adjacents, hold the cube so the front-upper and right-upper need
to be twisted and:

    2r2f2r2frau2rufru2fauf

    For two opposites, hold the cube so the front-upper and back-upper need
to be twisted and go:

    lafualfabuarfaurafbau

    For twisting all four, hold in any orientation:

    2r2b2r2uralblar2u2r2b2ru

-----------------------------------------------------------------------------

               CATALOG OF PROCESSES DISCUSSED

-----------------------------------------------------------------------------

    The file solve.h contains all of the strings used in the program.  Most
of them have probably never been published before since they were discovered
by my c128 computer.  Most of them are not useful to human solvers.  The
following are all that are necessary for a human to solve in under 2 minutes.
If you are out for speed, you must make yourself a racing cube.  Take one
apart and file all the edges down until it turns easily and smoothly.
Lubricate the center area only; otherwise the lubrication will get all over
your hands.  It will also pick up dirt if you don't wash it regularly.
You must also memorize some more of the processes that can be found in
solve.h, particularly the ones dealing with the last 4 edges.

    I)    No strings given for upper edges.

    II) Upper corners

    aradr
    fdaf
    ardrf2daf

    III) Middle layer

    urauarauafuf                   upper front to right front
    aualulufauaf                   upper front to left front

    IV) Switch two corners.

    ruaraf-au-frauar-2u               adjacent
    ruaraf-2u-frauar-(whatever is necessary)   diagonal

    V) Twist three or four corners.

    araurauar2ur-2u                twist 3 counterclockwise
    ar2uruarur-2u                   twist 3 clockwise
    araurauarurauar2ur               twist 4 (only picture 4)

    VI) Place last 4 edge pieces.

    rl2uaralafab2ufb               switch opposites
    2f2bad2l2f2bd2f2b               switch adjacents
    2rufab2rafbu2r                   cycle 3 clockwise
    2raufab2rafbau2r               cycle 3 counterclockwise

    VII) Twist last 4 edges.

    2r2f2r2frau2rufru2fauf               twist 2 adjacent
    lafualfabuarfaurafbau               twist 2 opposite
    2r2b2r2uralblar2u2r2b2ru           twist all 4