The Ideal Solution - Rubik Rubiks Rubik's Cube - Scanned Book-1981

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    AJ,;ki I:UBE ';UZZLE.an Introduction and Solution

    Welt, now that you have expertericed the challenge otRubik's Cube and lost, Y O u know why we say It's sodiabol'icall and perplexing., Oheer ' U p l ! lin order to Ihelp YO Uregain your sani,!y. we have developed the following simpleapproach to I'he ultimate solution of the Cube, Take heart-

    with a little practice and some memorization we will sohave yOU! dazzling your friends, relatives and tostrangers with your new found mastery of Rubik's Cu'You can tell them you took a short course in group theand linear algebra.The solution to :Rubilk's Cube requires. concentratlenandfaithful attention to the detailed tnatructtons in each ,Pari..lit should take you about an hour to read Ine directions andsolve the Cube mechanically. However, II you repeat theprocess several Umes, you willi begin to understand Ihowand why each group of moves work. You may even developyourown approach 'to the solution.

    There are 26 small sub-cubesthat make up a whole cube. ------.

    (A)

    We sug:gest that you memorize the groups o~movesthat you learn to solve the Cube without the directionOnce you can solve it on your own, the f'un really beginsyou try 10 do it laster and faster,Rubik's Cube can'solved in2rhinUItes flat, so have fun!To solve the Cube, you must first understand all of the coponent parts of the Cube and master a f'ew basic moves.

    colors, 12.middle egge pieces with 2 colors and 6 centwith 1 color each (see figure B) ..In the ultimate solutioneach sub-cube has only one correct rocatlon.

    Middle Edge piece2 visible colors

    Corneir piece~~-~ viSible colors

    2.PERSPECTIVES------------------------------------------------First, to make sure we are looking at the cube In thesame way we must agree what to call each side:

    1.1:HECUBE----I11111!!!!!!!!----------------------BaS'i~ Cube Parts Rubik's Cube is a . deceptively innocentlooking 2 1 1 4 "curbs with over 3 billion possible color corn-binationS" It has 6 sldes, 6 colors, and 26 smaller subeuoes (see figure A,) . There are 8 corner pieces with 3Figure 1

    Center piece1 visible color ---;

    Top can only turnleft or RIght

    'f ~ ~- ' v -I/ V//

    Front can only turnClockwise orCounter Clockwise

    Left can only turnup and away o r towardyou and down

    If ./"I/4 J IV

    Figure 2

    L /" LL.Ji"IvV 'V1/V VV

    All turns are either 90 (1turn) or 180 (2 turns). IDEAL TOVCOHPORATION 1980, ALL RIGHTS RESERVED.

    Right can only turnup away or towardyou and down.

    Center can turn up &away, toward yOU' &down, 'I,eft & ~igh!,and ctockwise 0 "counter ctcckwtse.(An easy way to dothis is to move thecenter and the :right.side up & away 10gether, then movejust the rigfH sid'eback down one turn) ..

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    3. COLOR ALIGNMENTColor Alignment is an important concept to understand,and it is illustrated in figures 3A and 38. A completed cube(A) has all its pieces color aligned. Now imagine popping

    (A)Completed cube.All piecescolor aligned.

    out. one sub-cube, then putting it baok in with ireversed, This piece wou'ld now be In co rr ec t pono t co to r a lig ned. (See (8) .below) ..

    Figure 3 ;:/:~::::.~I I I ~ ? (8)Ol.:#----This correcbut isaligne

    4.HOWITWORKS-------------------------------------------------A . The cube can be manipulated by rotating rows verticallyor horizontally, and just a few simple turns are required toproduce a completely random pattern of color.

    a. Horizontalrotation oftop row

    Figure 4

    b. Horizontalrotation ofmiddle row

    c. Verticalrotation ofcenter row

    C. In order to solve a side you must move certain cubesfrom vertical to horizontal planes, to line up rows of 3 sub-cubes of the same color. Note: one tu rn moves a sub-cube 3places.and 2 turns will move it 6 places:

    tst Move:Turn bottom to right2 turns

    2nd Move:Top down1 turn

    B. a) The center square on each side determinesof that side (See figure 5A).b) No matter how the colors are mixed, if yoto hold your thumb and forefinger on opposite

    pieces, they WOUld show you which colors appposite each other on the cube, e.g., if left centerthen right center must be green. (See figure 58).

    Figure 5

    (A) (8)

    Note: This may vary from cube to cube since eacmay be labeled differently.

    3rd Move:Bring red back byturning bottom left

    1 turn

    4th MoBring 3back on

    5.THEOBJECT---------------------------------------------------The object is to return all 6 sides to their original solidcolors, and there is lots of satisfying tun along the way as

    A. Solve one side inany fashion-You're a Star

    you sotve one or more sides to create inte.reslingpatterns of color. Here are the levels of skillyou

    B. Solve one sidecorrectly-You're an Expert

    C. Solve two adjacentsides-You're a Master

    D. Solve eight cornerscorrectly-You're a Grand 'Master

    E. SQlveal1Cong ratYou're 8

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    THE SOLUTIONWe will approach the solution by breaking it down into 5more manageable parts. These 5 parts must be done in thefollowing order:

    PART I SOLVE THE TOP CORRECTLY.PART II PUTTHE BOTTOM 4 CORNERSINTO PLACE.PART III COLOR ALIGN THE BOnOM 4CORNERS

    PART IV SOLVE 2 SIDES OF THE CUPARTV POSITION AND COLOR ALALL REMAINING OUT OF PMIDDLEEDGE PIECES

    PART I SOLVETHETOPCORRECTLY.-----------------------------------Before you begin to solve Hubik's Cube, you must firstlearn how to solve one side correct/yo Ironically, solving thefirst side is easy to perform but hard to explain becauseSOLVING THE BLUESIDENote: Solve for blue first so that we will be talking aboutthe same reference color. The other colors may not matchour diagrams since each cube may be labeled differently.Part I is divided into three sections:Section A describes two moves that will help you positionand color align the 4 blue corners.Section B gives you 5 basic maneuvers you will need tobring the 4 blue top middle-edge pieces up into posltlon

    the missing pieces are randomly dispersed overcube.

    and color aligned. These five maneuvers don't hdone in any order. You should learn them and usyou need them.Section C defines the starting position.

    A. Position and color align 4 blue corners. ----------------------Move the four corner sub-cubes with blue and the bluecenter to the top of the cube so that the blue squares ap-Figure 6

    If you cannot bring the four blue corners up into correctcolor alignment, then bring them to the top any way you

    If you bring up the blue corners in any fashion, one of 3things will happen.a) None of the corners will be in position.b)Two of the corners will be in position & color aligned, or

    pear on top. As you bring up the blue corners, trthem up into correct color alignment as shown in

    2 blue corners incorrect position.Note matching yellowside edge colors.

    can. We will show you how to exchange them sofall into correct position and color alignment.'

    c) All 4 corners may fall into correct color alignmeaccident. In this case, you go on to Section Bon p

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    a. If none of the corners are in position, keep the blue refer-ence corners on top, and follow steps 1-9 below.,Note: TheX'ed corners are the ones that will exchange.

    L ./ ./ ./,1/

    I' ,I'VI,r ' ,I'VStep 1Left SideDown

    ./I';~ j"

    vV\ /V,Step6Left sideUp

    ./ ./VVII1 " , ( 1 1V

    Step 2Bottom Left

    Step 7Front CounterClockwise

    ./' ./ ./ ./I)~ /1

    ,I'/,I'V. 'tep 3Right SideUp./VVIt'

    ~~-tepSBottom Left(2 turns)

    L L/'"' "~It'

    Step 4Bottom Left

    Step9Front Clockwise

    'StepRightDown

    Figure 7b. If two of the blue corners are in position and coloraligned, the remaining two incorrect blue corners must beexchanged. Keep the blue reference corners on top, andturn the whole cube until the two incorrect corners faceyou as shown in figure 7 at right. Now. follow steps 1-10below.

    _r---..,..---- 2 correctcorners

    Nole: Grasp the non-moving 2 thirds of the cube firmly tomaintain your starting orientation (blue on top). The X'ed(incorrect) corners are the ones that will exchange.

    . . . -I: I I V

    I, Vh , . IIVStep 1Left SideDown,

    " -- - . > ~

    Step 6Front CounterClockwise

    ./1/~~. . ,[;lIV

    Step 2Bottom Right(2 turns)

    ./VIIIIViti

    .J ~ ~vStep 7Bottom Left(2 turns)

    Li- " /,1'

    ,/I ' /,I'VStep3Left SideUp

    Step 8Front CounterClockwise

    Step4Front Clockwise

    L ./ ./ .//V

    VV< .. , . . . . . VVStep 9Bottom Right

    .JStep 5Bottom

    Step 1' 0Front Clo

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    A t this point, you should have 4 blue COrners in positionand color aligned as shown in figure 8.Now you must position and color align all 4 top middle-edge pieces.Note: All 4 pairs of side edge colors must match up. ---+~J_~-l

    -r,_~~-------TopMiddle-edge

    piece

    B. Solving the four blue rniddle-edqe pieces. -------------------The correct top middle-edge pieces wi II be found inane ofthree places: on top, either in position or out of position;on the middle row or on the bottom row.a. To bring up a middle-edge piece from the middle row asshown in figure 9, read the note below. Then follow steps 1 -4 below. (1)This is an out of place-----====j-

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