the ideal solution - rubik rubiks rubik's cube - scanned book-1981

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  • 5/14/2018 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-

    top middle-edge piece onthe middle row.

    Note: Before you do steps 1-4, keep t he blue referencecolor on top, and turn the whole cube until an out of placetop middle-edge piece appears in position #2 above. Then

    //II~;'~ .-. . . . . / 1/1//Step 1Center Left(to save it offto the side)

    Step 2Right SideDown

    move the middle row horizontally until the piecefalls into position 1 1 1 . This is the correct startingfor this process. Now proceed to do steps 1-4.

    STOP!SeeNote,Below

    Step 3Center Rig ht(Moves back missingpiece in between2 blues from top).

    Step4Right(Moveback o

    Note: Proceed to step 4 only if the missing top middle-edge piece falls into correct color alignment as shown in

    step 3 diagram above.lf the piece is out of colorproceed to do steps 4A-4D below:

    ~.I" !.. , . 1/

    [ / 1 /

    .,/ I ;//I /1/, /1/Step 4ACenter Left

    Step 4BRight SideUp & Away (2 turns)

    b. To bring up an out of place top middle-edge piece fromthe bottom row, first move the piece you need directlybelow where it belongs as in figure 10, then follow steps 1-4 below:

    ~~-I

    /v1/Step 4CCenter Right(2 turns)

    StepRighDown

    Red onbottom ----~

    Step 1 Step 2 Step 3 Step4

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    c. You may find an out of place top middle-edge piece withthe blue reference color hidden on the bottom of the cube.Turn just the bottom row until this piece is lined up directly

    below where it belongs. See figure 11, then follow steps'3 below.

    r t-I . . ;l/V

    1 . , 1 / 1 /1 /

    1 . . ; 1 . 1

    l/~4 - 1 1 1 " ' 1 11/

    Step1Center towardyou and down

    Step 2Bottom Left(2 turns)

    LL Z " "I' I/V1/[ / 1 1"tep 3Center Up

    & Away

    d. You will sometimes find top middle-edge pieces that arealready on top but must be exchanged in order to fall intocorrect color alignment. See figure 12.

    To exchange the two top middleedge pieces shown infigure 12 fallow steps 16 below. Note:: X'ed pieces are tn eones that will be exchanged. Keep blue on top../

    vIIiV1/

    ,~ i I I V '

    , ../'" I/

    '"I' ,1 [ 1 1

    Step 1Center Down

    Step 4Center CounterClockwise

    I l/VViii

    I I i V'll

    1 : . , , 1 . 1

    )'< I l l -~~

    Blue & yellow middle-edgepiece must exchange witblue & red piece to be incorrect color alignment

    Step 2Center Clockwise./ 7 7 7

    I/V

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    If you practice solving one side correctly. you should even-tually be able to put all 9 pieces of any color into correct color alignment in less than one minute. Thepractice the less you will have to depend on the

    C. The starting position defined. ------------------------To begin salving the whole puzzle. first solve the blue sidecorrectly, but leave one of its middle-edge pieces un-solved. This IS known as the STARTING POSITION. (Seefigure 14 at right). The missing piece will act as a guide inPart IV.Note: Except for the blue reference color. we won't refer tospecific colors, since they don't matter. and each cubemay be labeled differently.Now that you have solved one side of the cube correctly,you have actually solved lh of it. At this point you are In theSTARTING POSlTION. and you are ready to proceed to PartII since you have 4 of the corner sub-cubes in correctposition and color aligned on the solved side.

    Referenc(blue) on

    Missing guidepiece (any color) ~~-+ ....

    Figure 14

    PART II PUT BOTTOM 4 CORNERS INTOPLACE---------------The object of this part is to put each of the 4 remainingcorner sub-cubes into its proper place (but not coloraligned).A. Hold the completed blue side away from you. This is im-portant. Throughout Parts II and III the completed Sidemust be held away from you (at the back of the cube) at alltimes! See diagram (Figure 15). This next process exchanges Bottom Left Corner (A) with Bottom Right Corner(B).While holding the completed Side away from you. examinethe 4 corners of the cube facing you (the front 4 corners.(ABC & 0). Check to see if any 2 or all of them are in correctposition. You will a/ways be able to lind either 2 or 4corners in correct posttion. If you only find one or you findnone. then rotate the front face of the cube and check again.

    A corner is in correct position only if all 3 of its colorsmatch all 3 of the colors of the center squares it touches asin figure 16A below. Figure 16A shows the top right corner

    Figure 16A/' /" /'/" .//' /' /' ./

    ; - . _ ~~U~ V~IIV II/V

    This is an example of acorner In correct posit ionbut not color aligned.Notice the corner is red,green and yellow and the 3center squares it touchesare red, green and yellow.

    If you find al14 front corners in correct position, then go onto Part III, If you find 2 corners in correct position they willeither be side by Side (in A&B or in D & C) or diagonallyacross from each other (in A & Cor D & B). See figure 15above.

    Keepblue

    I DFRONT

    A BFigure 15

    in position but not color aligned. Figure 16B shsame corner in position AND color aligned.

    Figure 168

    This is an examplesame corner in corposition AN D colored. Notice red toucred, green touchesand yellow touchesyellow.

    Remember, you must a/ways find 2 or 4 of the froin correct position. If you find none or only onthen keep rotating the front face of the cube and4 front corners after each turn unti I you fi nd 2 or

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    / .// / ./ ././ ./ ./ ./1./ VVV i o ll/ 1 IVx , X 2 l/

    1 0 . I

    B.lf the 2 corners in correct position are next to each other(in A & B or C & D) then you must exchange the other 2remaining front corners. To do this, turn the whole cube

    Figure 17

    until the 2 incorrect corners appear in the X'ed pshown on figure 17. Keep the completed blue sand follow steps 1-8 below.

    Complete blue Sidein back.

    2 incorrect corners to be exchange

    C. If the 2 corners in correct position are diagonally oo-posite each other (in A & Cor D & B) then you will have torepeat steps 1 -8 twice. Follow steps 1 - 8 , then rotate thefront face of the cube one turn clockwise or counterclockwise and check the corners again. Now you shouldfind 2 corners side by side in correct position. To exchangethe remaining 2 out of place front corners, turn the WHOLECUBE until the 2 incorrect corners appear In the X'edpositions as shown above in figure 17. Now run steps 18again.

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    solved blue side at the back (away from you). This 8 step

    INITIAL ORIENTATIONa. If after you complete Part II, you find you have one of thecorner sub-cubes color aligned, turn the whole cube sothat that corner appears in the position marked (X). Dosteps 18 below.

    b. If you have two corners aligned, then turn the wholecube so that they fall in the position marked (A) and (6) or(A) and (C). Do steps 18 below.

    c. If none of the front corners are color aligned then itdoesn't matter. Do steps 18 below.

    This process must be repeated several times (usually 2 to 4times) until all 8 corners are color aligned with reference totheir center cubes.Check for color aligned corners each time you do steps 18,then refer to a, b or c above before repeating the process.You will know that all 8 corners are in color alignmentwhen every side of the cube shows at least 5 squares ofthe same color in an "X'ed" pattern. See figure 1 9.

    Remember, first check how many corners are color alignedto make sure you are in the correct starting position. See a,band c above. As you do the procedure, be sure to grasp

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    PART IV - SOLVE TWO SIDES OF THE CUBE ----------------The object of this part is to solve 2 opposite sides of thecube by using the guide piece to solve one bottom middle-edge piece at a time,When you solved the first (blue) side you were instructed toleave one middle-edge piece out (unsolved), This missinq

    piece will now act as a guide piece. See figure 2Turn the whole cube so your blue reference coon too. Keep blue on top and turn the whole cubti I the guide piece is faci ng you as in figure 20 A

    A. Choosing a Target Piece -------------------------Now turn just the bottom row of the cube until an out ofposition bottom middle-edge piece appears directly belowthe quiae piece as In figure 20B. This is the TARGET pieceyou will solve, Notice the two common colors of the 2lower front corners. In the example in figure 20B the twocommon corner colors are yellow and orange. This meansthat the correct bottom middle-edge piece for this spotmust be yellow and orange, In this case, the correct pieceis located on the middle tcr.

    Blue on

    Figure 20A

    Notice the guide pieceIS directly over an out of positionbottom middle-edge piece (white & green). -----.,--'-----;-.-

    ......,__~r-Correct bottom middle-edge piece torth!s2 common colors I--''

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    ./

    < - /,/I //

    Step 3ACenter RightStep 38Front CounterClockwise (2 turns)

    b. If you find the CORRECT MISSING piece on the bottom,first, turn just the bottom row until the correct missingpiece appears under the GUIDE piece. (This will move your

    "c VVV 'V//Step 1Front CounterClockwise

    Step 2Center Right

    L ./ ./ "lV ,I/~

    ..tIL ~ IIVStep 3CCenter Left(2 turns)

    Step 3Front CClockwiTARG ET piece out of position temporarily.)steps 13 below.

    Step 3F:ront Clockwise

    Note: After Slep 3the CORRECT missmc pwill be stereo In positionas shown In step 3.

    NOW TURN THE BOTTOM ROW UNTIL THE lARGET PIECE APPEARS UNDER THE GUIDE PIECE AGGo back to section fBa) above and follow steps 130f 130.c. If the correct missing piece is the guide piece then follow steps 13 be/ow:

    L /' Z / ,

    < vi-''" V II!/Step 1

    Front CounterClockwise

    Step 2CenterRight

    IISTOP!.I SeeNoteBelow

    Note: Do net go on to step 3 unless the miss'i;ng piecedrops into correct color alignment afte,r step 2. If after step2, the missing piece appears in position but out of colorallignment. then go back to section (A ) above and followsteps 3A

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    TOp (Reference Color) Blue(1) Guide piece

    ~-~~-(2) Correct Top Middle edge pie--i~ __ '-------- (3 ) Bottom middle

    edge piece color aligned"'~~~~r-.--------Bottom completely solvedFigure 22

    2 '/i/'1 3 .I/.I/

    r-.I'r-,1'" 2 /~r - . . 3 J" - " /'\ V'\ V

    Step 1Front CounterClockwise

    Step 2Center Left

    1 )/3 /V

    V/

    11', 3 ...v/r - . . 2 V" - /'\ V V'\

    " r - - . . . / /' /''~ 3'\h..~",Step 3Front Clock-wise

    Step 4Center

    L1 /V':-3.I- ",2 [.IVV

    I V

    .-. . . . . . . : : "7'v I, V I

    1 /, / ), I ' 3 /)

    Step 5Front ClockwiseNote: If after step 7 the gUide piece falls Into position butIS not color aligned, REPEAT STEPS 1-7 THEN TURNCENTER ROW RIGHT 90" ami REPEAT STEPS 17 AGAIN.

    Both top and bottomthirds are completelysolved.

    Step 6Center Left Step 7Front Counter Clockwise

    Now you should have both the top and the bottocube completely solved as snown in figure 23, wittop.

    Figure 23

    PARTV-POSITIONANDCOLORALIGNALLREMAININGOUTOFPLACEMIDDLEEDGEPIECES.-----------------------New OrientationTurn the whole cube so that the 2 solved sides appear on t he left and right sides. See figure 24.Keep this new orientation fixed, and turn just the cenler upand away until all 4 remaining center squares fall intocorrect color alignment as in figure 24. Note: Blue on leftside.At this point, you will find one of five things will happen:

    Case 1 Four middle-edge pieces out of place and not coloraligned. Use process (A) on following page twic_e.Case 2 - Three rniddle-edqe pieces out of place and notcolor aligned. Use process (A).

    Case 3 Four middle-edge pieces in position but not coloraligned. Uses process (B) on page 14 twice.

    all centers Incorrect color al ign

    Case 4 Three rniddle-edqe pieces out of placepiece in position but not color aligned. Use prthen process (B).Case 5 Two rnloole-edqe pieces in position butaligned. Use process (B).

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    A . P r o c e s s A - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -The goal of Process (A) is to place all remainmg unsolvedmiddle-edge pieces into their correct positions.The four step procedure outlined below will move threemiddle-edge sub-cubes, causing them to exchange theirpositions with each other, without disturbing other sub-

    cubes. Figure 25 shows the three side sub-cube!xchange positions. The position exchangefollows: the side sub-cube marked 1 will mposition occupied by side sub-cube marked 2; thcube marked 2 will move to the position markedside sub-cube marked 3 will move to the position1

    L1/

    - "!/,3 )'

    Figure 251 moves to 22 moves to 33 moves to 1

    Starting Posit ion

    Now check all the remaining out of place middle-edgepieces and pick 3 that will fal; into correct place if ex-changed.

    Be caretut to maintain the starting crlentatlon when usingthe procedure, hold both solved outside thirds firmly insteps. 1and 3 .

    I I ~ v , . . .,I - "1/1 . . .V"

    , : ~/,/I!/I/Step2fop Right(2 turns)

    Step 1Center Up& Away

    Repeat Process (~) steps. '-4 above untlleither the puzzleis solved OR you find you have left one pair of m~ddle-edgepieces that are In position but not color alig,ned. To solvethis last pal,r go on and do process (B ) steps 1-12 below.

    :Remember, first find the 3 out of place middle-ethat. wiill fall into correct position it they are exthe manner below:

    -'vV 'V

    , V~ VV

    ,

    ,

    Step 3Center BackDownStepTop R(2 turn

    If you find you are in Case 4, you will have 2 pairsedge pieces in position but not color aligned26A. Process (B) will solve them one pair at a tim

    Figure 26Ashows a pair oftop middle-edgepieces in positionbut notcolor aligned.(Before Process B).

    Figure 26Bshows that samepair color allg ned.The whole cube issolved. (AfterProcess B).

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    B. Process B ------------------------------ThiS t2 step process Is known as Rubik"S Maneuver afterErl"i()Bubik, the'jnvento:rof the Cube. 8efore you run Process (B), the 2 middle-edge piecwl'losecolors are to be flipped must be opposite eaother on top of the cube as shown in figure 26A.

    L L / /1I l , o j ~ l/ViI V'~l V1 V,I \ V / /' /. . . V'/,/1//V

    I

    IJ ~ v V// ' 1 ///. .Step 1Center Up& Away Step 2Top Right Step 3Center Up& Away, ~ vV. VV

    VV

    L I~. . . .VV/1/ V/

    Step 4Top Right Step 5Center Up& AwayStep 6Top Right(2 . turns)

    L /1( / / v -I //I )'/ III'- V/Step 7Center BackDown

    Step 8Top Right Step 9Center BackDown

    . . . , . . " * " v/)"/ II//

    / 1//V 1/// 1/''- /

    L / / /1', ~VVVII

    Step 10Top Right Step 11Center BackDownStep 12Top Right(2 turns)

    Repeat Rubik's 12 step process if you have another pair inposition that needs to be color aligned. Now you have solved the cube- Congratulations, you'reCUBIST! Mix it up and start again,

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    T H ES O L U T I D N