ll is guorcnl,eed io work.No motter how bodly your cube is scrombled, this solu-tion provides every stepfrom beginnirrg to end to restoreit to solid colors on oll 6 foces. Every step is provided in oneosy-to-follow sequence. The solution does not involveoiml'ess moves, noi is it necessory thol the cube be holfsolved to begin moking moves.

ll offers cleor qnd sleady progress.The solution siorts wiih the top foce (whbh you choose)ond proceeds steodily to the bottom foce. This solutionhos been designed so thoi very little of the previouslycompleted portion of the cube need be disturbed toproceed. ln other words, ofter you hove completed onefoce, you will need to disturb very little of it to continue,ond then only tempororily.

ln generol, no more thqntwo previouslyplocedcubeswillbe more thon one move owoyfrom their proper position.h is, however, very importont to the solution lhot youreolize (ond occept) the foct ihot temporory disruptionof hord-won progress is necebsory. lndeed, it is proboblythe most difficult ospect of solvirg the cube for thefirst time,

ll pesenb few qnd uneomplicoteddeclsions.At some of the steps in the solution. it is necessory tomoke decisions in order to proceed to the correct nextstep This solution hos been designed so thot these deci-sions ore os few ond uncompicofed os possible, Whensuch decisions ore necessory, illustrotions ore frequenflyused to focilitofe understondirg. You willhove to moichthe pottern of colors thot occur on your cube to one ofseverolillustroted potterns in order to decide on the nextstep.

ll qllows lor etror.The sequences of rnoves ore designed so thot if youmode on error (such os turning o foce the wrong woy.qetting lost in o sequence of moves, or even dropplngthe cube in the midst of o sequence) you willonly hoveto retreot one siep insteod of storting over. lt is veryfrustroting to discover oi the lost step of o solution thqtthe cube is os bodly scrombled os it wos when youstorted. Conecting on error is mode eosy becouse solittle of the previously completed ports of the cube oredisturbed. This book provides sequences of moves thotore designed to deolwith the most common errors.

ll fecrlures eqsylo'memorizesequences ol moves.It is possible to solve cny storting orrorgement of thecube by o few similor sequences of moves, lt is eosy toget used to these moves. They consist of similor sets of 3to 5 foce turns ihot ore done repeotedly'

The required moves ore set in bold fqce ond oredesignoted with o double osterisk (") throughout. This

mokes memorizing the solution simpler. (lmpress yourfriends!)

ll is independenl d color.This solution is not coded by the colors of the foces. tt will

therefore work no mcrtter whot the 6 colors ore on yourcube ond how they ore distribuied on the 6 foces. ltwould be nice to present o solutkrn thot reod: 'Turn theoronge foce, then turn the red foce," etc. However, thereore vbrious monufocturers of these cubes. ond they dlchoose either different colors for the 6 foces or differentdistributions of these cobrs. (For exom$e, oronge is notnext to yellow on ofl cubes,) There ore 30 different woysof distributing 6 colors on the 6 foces of o cube.

tI

Etui"**--

Solutions thot use colors (ord they do exist) con onlywork for o specific colorirg of the cube' The nototionscheme used in this book is independent of color ond will

work for ony colorirg ond ony mcnufocturer's cube.

On the other hond. this solution dces not use the fewestnumber of moves possible, lt wcs intentionolly designedfor clority oncl involves the ieost number of uncompli-coied decisions rcther thon the fewesf number ofmoves. There qre mony stoges of which reducing thenurnber of moves is possible, ond these ore given cs shorlcuts. Nevertheless, with proclice, it is possible to solve rcn-dorn orrongemenis of cubes in under 3 minutes.

lf you would like c few hints before trying to soive o cubeproblem, recd only pqges 2l to 23.

Now enjoy your imoending victr:ry over thct infernolcubel

ABOUT THE RUBIK'S GUBE:A bdel hisloryThis fbscinoiing puzzle wos designed brl Erno Rubik, onorchitect ond teocher in Budopest, Hungory lt wos op-porently designed independently by Terutoshi lshige, onengineer in Jopon. Both opplied for potents in themiO-tgZOs. Professor Rubik designed the cube os on oidto his students in recognizing spotiol relotionships in threedimensions.

lf you hove olreody experimented with solving the puzzle,you moy wish you could follow the movements in threedimensions more eosily. lt is chollenging, to soy the leost,to estoblish the relotive positions of the smollcubes ofteronly 2 turns of different foces.

The cubes were first monufoctured in Hungqry ondbecome ovoiloble in Europe in 1978. lt is only recently thotthey hove now ochieved their substontiol worldwidepopulority (mony millions soldl), They hove been widelyovoiloble in the United Stotes only since ]980. lt seemsthot these cubes were olmost os common os ornomentsduring the l98O holidoy seoson.

IO

**---.1 -

How does il workilThe ingenious mechonism thot ollows oll 6 foces of thecube to rotote is so simpe one is tempted to osk, "Why

didn't lthink of it?'The difficulty is, of course, in figuring itoui for the first time.

It oppeors thot otlthe smoll cubes con move obout in

foct, however, only the cubes on the corners ond edgesoctuolly move. The center cubes ore fixed ond con onlyrotote in ploce, This is the key to understonding ihemechonism,

ROTATE TOP FACEI/8 TURN TOIAKE APART

EDGE CUBEWTH TAB

CORNER CUBEWITH TAB

ROUI{DED TABS OF CUBES

RIDE ALONG CURVED TRACKFORMED BY BACKS OF OTHER

CUBES IN EACH PLANE.

PRESSURE EXERTED BY EACIIHOLDS NEIGHBORINGCUBES IN PLACE. THIS

RESPONSIBILITY IS SHIFTED

TO THE NEXT ADJACENT CUBEWHEN CHANGING PLANES.

IT'S INGENIOUSIPEEKING INTOTHE CUBE

CENTER CUBESARE FIXED ANDONLY ROTATE

IN PLACE

Eoch center cube is on the end of on oxle' lhe cornerond edge cubes ore not ottoched to onything ondmove obout the center cubes'

You moy osk, "Why doesn't it just foll oporf?" ln foct. it conbe token oport quiie eosily' Simply turn ore foce on+'eighth turn ond either pullout one of the edgecubes ontn6t foce or pry it out with o screwdriver. tt lelps to pull

the foce you'tuired owoy fiom the rest of the cube' The

remoining cubes con now be eosily removed to reveol

the centrol meclsrisrn.

The cube does not foll oport by itself becouse the edgeorxJ corner cubes hclcl eoch other in ploce in oremorkoble feot of cooperotionl lf you toke tle cubeoport this woy, be sure to put it bock together wtth solid

cbbrs on oll6 foces, Otherwise. you moy rsver be ott'eto solve the puzzle unless you toke the cube oport ogoin'

1312

6a---.a

Cube bqsicsThe cube consists of 6 fixed cubes, one in the center ofeoch foce, 8 movoble cubes on the corners (cornercubes) ond 12 movoble cubes on eoch edge (edgecubes). The corner ond edge cubes ore moved oroundby rototing the 6 foces.

Any corner cube ccn move to ony corner posiiion, ondony edge cube con move to ony edge position by o se-quence of foce rototions,

lbwever, eoch movoble eube belorrep in only ore bcc'tion. For exonrpb, the yelbw/whlte @e cube (mycube fus ore with these colors) belorg on the edgebetween the ye$ow ond uhite fqces,

The color of o foce is deflned by the color of the fixedcenter cube on thot foce. The yell,ow/ororge/whitecorner cube belongs on the corner joinirg the yelloworor€e, ond white foces.

14

q€rtr,

_15

A cube is soid to be ploced or positioled correctly when

it is on the cornerbi-edge w6eiSllTelongs' tt mov'

ho*euer, be ptoced correitty ond not be oriented cor-

t "tfy

n cube is soid to be oiiented conectly when it is

positioned correctly ono me coi6Fmotch those of the

Eoiocent center cubes. This is the desired finol situotion.

Wnen oll cubes ore positioned ond oriented conectly'

the Puzzle is solved. -

r.I

The methocidescribed in this book seporctes thg pr,oP

r.ti oipfocing onO orienting the.2O movoble cubes into: s steps- eocnLitne 5 steps-involves the plocement ond

oGni"tion ot a ci#s' ni ony of the 5 steps' cubes thot

noo. O."n ploced ond oriented in previous steps ore

only tempororily disturbed''

Thereisnoconcernoboutcubesinloterstepsuntilthotti"p it reocneO. tvtoreover, eoch cube in the first 3 sets is

' + 6r"E*l onO orienteO individuolly' ln reolity' then' the.prob-

ie* is broken upinto 12much smollerproblemsof plocing

onO'oti*nting iidividuot cubes' lt is onlv fgr tnqlgs]-Z

1e^!of 4 cubes t6ot more thon I cube must be poceo ono

+ orientedsimultoneouslY'

CORRECTLY POSITIONED

AND ORIENTED

tik

ll

4

rl

tlIt

t1

rif{

CORNERS: CORRECTLY POSITIONED

BUT INCORRECTLY ORIENTED

CORRECTLY POSITIONED

AND ORIENTED

For exomple, the cubes on the iefi show correctly posi-

iCn"O "Cg*

snd corner cubes that ore inconectly

"ri""t"O. TXe cubes on the right show these edge ond

corner cubes. correctly positioned ond correctlyoriented.

t6

EDGES: CORRECTLY POSITIONED

BUT INCORRECTLY ORISNTFD

17

-.i

.4

suMilAnY oF $OturpltA summory of tl'egrererclstrctegyof the 5 sleps f&ws:l. Cf,oose your fovorite c& of the 6. plqce qnd orient

the 4 edgs cubes on the foce with yor.r fcnrortte otthe center.

2. Hoce snd orient the 4 corner cubes on the top foce.

3. Roce ond orient the 4 sideedge cubes of the middleloyer. All 12 cubes ploced in steps l-3 ore ploced ondoriented individuolly, The top two{hirds of the cube isnow complete.

4 Hoce ond orient the 4 corner cubes on the bottomfoce.

5. Hoce cnd orient the 4 edge cubes on the bottomfoce.

ln eoch of the 5 steps, there ore generolly these 2substeps:

l. noce the cube(s) in the proper position,

2. Orient the cube(s) conecfiy. This requires o tem-porary removolof ony cube from its correcl positionond its subsequent return to the proper po$iion in theproper orientotion.

I. TOP FDGES 2. TOP CORNERS

3" VERTICAL EDGES(one more in bcck)

II. BOTTOM CORNERS 5. BOTTOM ED(

SUMMARY OF THF PARTITIONING OF THE 20 MOVABLE CUBES FORTHE 5 STEPS OF THE SOLUTION. AT EACH OF IHE 5 STEPS

THE 4INDICATED CUBES ARE POSITICNED AND ORIENTED.

l9t8

5. BOTTOM EDGES

Why does this solulion wod<?The difficulty of the puzzle is perhops mode mosiopporent by noting thot there ore slightly more lhon 43quintillion (4.3 x lOl'g) orrongements possible for oll 20movoble cubes.

How big is 43 quintillion? Well, the notionoldebt in penniesis "only" IOO trillion. The oge of the universe in seconds is

thought to be only obout 5 quintillion,

A very fost computer would toke centuries to exomineeoch orrongemenf. Yet by leorning this solution ond withproctice, you will be oble to solve the cube in o fewminuteslHow is this possible?

The odvontoge of this solution method is thot by designof ony time during eoch of the 5 steps. one is concernedwiih very few of the cubes involved ot thot step, This

simplificotion is possible becouse there ore fewer or-rongements possible for 4 cubes (the most thot ore everbeing deolt with ot one time) thon for 20 cubes, ln foct,much of the time (steps 1-3), only o single cube is beingdeolt with, lt is not difficult io keep trock of just one of the20 cubes,

ln oddition, the problems of positioning ond orientingcubes ore done seporotely, which significontly reducesthe number of possibilities. Since there ore so few or-rongements of the cubes of concern of ony time, it is

possibleto pxesent them cillond providethe crppropriqteoction for eoch.

These cloims con be mothemcrticolly proved, so this solu-tion is guoronteed to be successfulfor solving tl'e cubefrom ony storting orrongement nc motter how bodlyscrombled.

Pleose do not remove the colored potches from thecubes ond reploce them differently or toke the cubeoport ond put it bock together inconectlylThis con bedonel lf you do this, you will not necessorily be oble torestore the cube to solid colors on oll 6 foces even if yououtlive the universe.

20

$horl culsAfter you moster the cube with this solution, you willprobobly think it is toking too long-ollof 5 minutes withproctice. For those on the fost trock. short cuts o.re pro-vided. These vory from simple seguences of moves toexpert short cuts thot chonge the overoll strotegy. Mypreferred method of solution uses these short cuts, ondlcon often solve rondom cube problems in under I min-ute. Ambitious reoders moy wish to improve on this

further.

Short cuts cre ploced in boxes of the end ofeoch section.

iholore ptoced cnd oriented in previous steps. For ex-omple, ofier one foce is completed, there is no woy tooccomplish onything more without tempororily dis-turbing some of the cubes on thoi now completedfoce. You must be doring enough io be willing to tem-pororily undo hord-won progress in order to continuewith the solution. I found this to be ihe most difficultport of solving the cube for the first time, For thisreoson, the solution in this book wos intentionollydesigned so thot very little iemporory disruption ofprevious progress is necesscry.

Hints. Remember thot the center cubes on eoch of the 6

foces do not move, They con only rotote in ploce, This

, meons the proper color for eoch foce is determinedby the color of the center cube on thot foce, For ex-omple, the foce with on oronge center cube musteventuolly be enlirely oronge,

o The overoll strotegy of this solution is given in the sum-mqry on poge 18 ond

.l9. This puzzle is too difficult to

solve wilhout some overoll strotegy. Try io follow the 5steps ond remember thot it oflen helps to correctlyposition o cube first and then orient it so thot thecolors ore correct,

. As you proceed tn sotving the cube, it is obsolutelvnecessory io disturb tempororily some of the cubes

1

farffnb..

21

o Do not concern yoursetf with cubes thot must bepoced of loter steps while workirg on eorlier steps.For exomple, while competing the top foce, don'tworry ot oll obout whot hoppens to cubes on the bot-tom foce, No motter how bodly the cubes involved inloter steps ore scrombled. it will olwoys be possible toploce ond orient them properly when their turncomes. There ore no "deod ends."

o Simpe 3-turn sequences of the type shown below orebosic to steps 2-4 of the solution. You simply rototeone of the side foces one quorter turn in either direc-tion, then rotote the bottom foce, ond then reverseyour first rototion, The sequences of moves requiredto occomplish steps 2-4 ore just combinotions of 3move sequences of this type, The sequence shownbelow chonges one top corner ond one verticol-edge cube without disturbing the other top-edge,top-corner, ond verticol-edge cubes, A greot deolccn be occomplished by just performing voriouscombinotions of these sequences.

e The simple 4*move seguence shown bekrw ollowsyou to monipulote edge cubes without disturbing onyof me corner cubes, Combinotions of sequences ofthis type ore most useful in step 5 but con be used ineorlier steps Q ond 3).

LEsl chsnceif you wish, you moy try to solve the puzzle with only thetoiegoir€ informotion. The remoining poges &scdbe ocomplete ond certoin solution for ony stortirg oronge-meni of the cube. Reodirg them might &stroy the en-joyment of working out o-solution yoursetf with jusf thefew hints olreody Provided.

'23

a

4,'

rR+

R-

n2

F+

F-

F2

L+

L-

L2

B+

B-

82

T+

T-

T2

P+

P-

P2

Turn R foce one quorter turn clockwise

Turn R foce one quorter turn counterclockwise

Turn R fcce one holf turn(either woy, it does not motter)

Turn F foce one oucrter turn clockwise

Turn F foce one quorter lurn counnerclockwise

Turn F fcce one holf turn

Turn L foce one cuorfer furn clockwise

Turn L foce cne quorler turn counterclockwise

Turn L foce one holf iurn

Turn B foce one quqrter furn clockwise

Turn B fcce one quorter turn counterclockwise

Turn B foce one holf turn

Turn T foce one quorter turn clockwise

Turn T foce one quorter lurn counterclockwise

Turn T foce one holf turn

Turn P foce one quorter iurn clockwlse

Turn P foce one quorter turn counterclockwise

Turn P foce one holf turn

FR is the edge cube on the edge between the F ond R

foces of o porliculor time. FRT is the corner cube on thecorner common to the F, R, ond T foces of o poriiculortime. The 12 edge cubes ore therefore BF, BL, BP, BR, FL, FR,

FT, LP, LT, PR, PT, ond RT. The 8 corner cubes ore BFL BFR, BLP,

BPR, FLT, FRT, LPT, ond PRT, Moves ond the cubes involvedore described using this terminology'

ln order to use the moves os written, it is necessory tohold the cube so thot the cubes thot ore to be movedcorrespond to those given in the description of the move.For exbmpe, if you wish to ploce on edge cube in the PT

position ond the sequence of moves given is written forthe FT position, you must rotote the entire cube in your

hond so thot the (former) PT position becomes the FT

position. Note: by doing this, the color of ihe F focechonges, but the color of the T foce remoins the some.

KEEPING THE FI?ONT FACE ORIENTED TOWARD YOU-ALL

CLOCKWSE I?OTATIONS ARE SHOWN, TO MAKE COUNTER-

CLOCKWSE TURNS, SIMPLY I?OTATE THE FACES IN THE

OPPOSITE DIRECTIONS.

ALL ROTATIONS SHOULD BE MADE AS THOUGH YOU WERE

VIEWNG EACH FACE FI?OM THE FIIONT, A CLOCKWSETURN WOULD ALWAYS BE A TWIST TO THE RIGHT AS IF

VIEWED FI?OM THE FTiONT. SEE THE |LLUSTRATIONS BELOW.

a

27

To fomiliqrize yourself with the nototion ond terminologyforthe cubes ond moves,look otthe sequenceof moves

' on ihe oppsite poge,You moy wish io duplicote thissequence with your cube, I suggest choosing o dorkcolor (e,g., blue or green)to conespond to the dork color

i on the drowing of the highlighted individuolcorner cube'

The first move is o clockwise quorter turn of the R foce(cube I to cube 2 on the opposite poge). lt is symbolizedby R+ ond tokes the highlighted corner cube from theFRT (front, right. top) position to the PRT (posterior, right,top)position.

The secondmevg (cube 2tocube 3) is o holf turn of the T

foce ond tokes the Nghlighted cube from PRT to FLT'

The third move is o clockwise quorter turn of the left foce.tneEofrercGe moves from FLT to BFL,

The lo3fh pgvq is o clockwise quorter turn of the B foce.The corner cube moves from BFL to BFR.

The fifth rnove is o counterclockwise quorler turn of the F

toceJne corner cube moves from BFR bock to FRT

where it stcrted, bui note thot the orientotion is different"

I suggest trying them to get used to the clockwise ondcounterclockwise rototions for the vorious foces, por-ticulorly the B, R, ond L foces, which ore used repeotedly.No rototion of the P foce is shown since it is never used' (i

find it too difficult to turn this foce while holding the cubeneorly fixed during o sequence of moves ond hovetherefore not included it in ony moves.) Try to duplicotethis sequence on your cube, Although this porticulor se-quence is never used in the solution, it indicotes how it ispossible to'totote" o corner cube to q different oriento-tion by o sequence of moves. A trick to developing osolution is to discover sequences thot do this withoutscrombling previously ploced ond oriented cubes'

R+

+

t2 (PRt)

<rt'

L+

+

{r'*

F-

++

I

4 (Brt) 3 (FH)

5 (BFR) 6 (FRr)

28SAMPLE SEOUENCE OF MOVES

29

A cube is doqeglor pggllgned correctly when it is on theedge or corner with colors the some os those of thecube. A cube is oriented conectly when the colorsmotch those of odjocent center cubes. For exompe, thecorner cube colored oronge, white, ond yellow (n mycose) is ploced correctly when it is on the corner odjo-cent to the oronge, yellow ond white center cubes. Thiscube is oriented correctly when the oronge foce is odjo-cent fo the oronge center cube.

To memorize q solulionSome sequences of moves ore set in boldlroce ond oredesignoted with double osterisks (")To memorize o solu-tion, you only hove io memorize these sequences ondfollow the instructions in sections thot ore olso morkedwith o double osterisk.

STEP 2: TOP CORNERS (FLT, FRT, LPT, PRT)

TOP FACE

The purpose here is to position ond orient the 4 cubesthot belong on the corners of the T foce ond moiniointhe previously ploced top-edge cubes. Top-edge cubeswill be moved tempororily during moves but will beproperly returned,

For eoch of the 4 cubes thot belong in one of the top.corner positions, do the following 6 steps (2A-2F). Agoin, ityou ore lucky, some of the top-corner cubes will be cor- "

rectly positioned ond oriented when you siort. ond youwill hove to do these steps fewer thon 4 times

2A. Locote o top-corner cube (thot is, one cornercube thot belongs in o top-corner position) thot is

not currently correctly positioned ond ortented.This is the desired cube, lf the desired cube is cor-recily positioned but inconectly oriented, go tostep 2E.

t,i

{I'

30 35

28. r tne desired cube is cunently on the T foce, do thefollowing sequence. Hold the cube so the desiredcube is in the FRT position,

"MoYe f{T to BFL: R- B- R+

This moves the desired cube to the B foce'

2C. Vtove the desired cube, which is now on the B

foce, under the desired topcorner position byrototing the B foce. Hold the cube so the desiredposition is FRT ond the desired cube is in the BFR

position,

2D. oo tne follpwirrg sequence of moves to correctlyposition the desired top-corner cube.

"Move BFR lo FRT: R- B- R+

2E. f tne FRT cube is inconectly oriented, do one of ihefollowing olternotive sequences,

"Orlenl FRT:Orient FRT:

Note thot the first sequence turns the corner cubecounterclockwise. The secoM sequence turns thecorner cube clockwise, As you goin experience,you will be oble to choose the proper one, How-ever, it does not motter which you choose for'now.

2F. ff the FRT cube is sfill incorrectly oriented, repeqfthe W sequence you chose in step 2E. This wlllteove ihe FRT cube conectly positioned ondoriented.

Remember thot you moy hove to repeot these 6 steps(2A-2F) os mony os 4 times to position ond orient eoch offhe 4 fop-corner cubes individuolly, Upon completion ofthis step, the top one-third of the entire cube will be cor-rect, I hope you chose o color you like for the iop foce;otherwise, you might be very tired of looking of it, ln onycose,lhope you ore not seeing'red" of this stoge; thereis stillquite o bit more to do.

Short culs

R- B2 R+ F+ 92 j-F+ 82 F- R_ 82 R+

L There ore two odditionol olternotive se-quences for moving o cube from BFR to FRT,

These puf the cube in on orientotion dif-ferent from the sequence in step 2D.

Move BFR to FRT: F+Move BFR to FRT: R-

The short cut is to decide when to use eochof the three possible BFR-Io-FRT sequences.You will be oble to ovoid the reorientotionsequence this woy.

B+ F-B+ R+ F+ 82 F-

2. Moue ony top-corner cubes thot stort outon the B foce up to their correct positionond orientation on the T foce beforebringirig ony cubes down from the T foce,Moving o cube frorn the B foce to the T

foce outomcticolly brings o ditferent cor-ner cube bock dowry on occosion. this willbe one you wont to bring down, onyhow.i

,.

i

;f,Fs6l.-g.^f'-\\\

37

FR R PR

B

STEP 3: VERTICAL EDGES (FL, FR, LP, PR)

LEFT FACE RIGHT FACE

The purpose here is to ploce ond orient the 4 cubes thotbelong on the edges odjocent to but below the T foce.This con be ihought of os completing the "middle loyer"or "equotor." After completion of this step, the top two-thirds of the cube is correct. For eoch of 4 cubes thotbelong in the verticol-edge positions. do the following 4steps (3A-3D). Agoin, you moy be lucky to find some ofthese verticol-edge cubes olreody positioned ond ori-ented correctly.

3A. Locote o verticol-edge cube (one thot belongs ino veriicol-edge position) thoi is not currently cor-rectly positioned ond oriented, This is the desiredcube. lf the desired cube is correctly positionedbut inconecily oriented, go to step 3D.

38.

3C.

lf the desired cube is noi on the B foce, do thefollowing sequence of moves. Hold the cube soihe desired cube is qt FR.

"Drop FR lo B toce (BP):R- B+ R+ B+ F+ B- F-

At this point. the desired cube is on the B foce,Rotote the B foce until the color of the verticoifoce of the desireC cube motches the color of thecenter cube on one of the 4 sicie foces. Hold thecube so the desired cuife beiongs in the FR posi-tbn. lf it motches on the [i foce, do ihe sequenceBi? tc FR. if it moiches on the F foce, do ihe se-quence BF to FR.

TURN PA€E FOR STARTINGPOSITIONS FOR MOVES INSTEP 3 CVERTICAL EDC+S).

-ILP L FL

LB

3839

The stcrting positions for these sequences ore shownbelow.

lf colors mcrtch on the R foce, use the sequence of movesBl? to FR.

"Move BR to FR:B+ F+ B- F- B- P- B+ n+

lf colors motch on the F foce, use the sequence of moves' BFtoFR

l'Move 3F lo FR:B- R- B+ R+ B+ F+ B- F-

STARTING POSITIONS FOR MOVES IN STEP 3(VERTTCAL EDGES)

/'\ 40j\ \i-" , \

3D. ttotO ihe cube so the desired cube is in the FR posi-tion. lf it is incorrectly oriented, do the foilowirgreorient sequence.

"Orienl FR (oll 15 moves):R- B+ Ri T+ F+ BJ F-

B+ R- B+ R+ B+ F+ B. F-

lf the 4 verticol-edge cubes cre not oll correctly posi-tioned ond oriented, go bock to step 3A,

Error eorrectionThese sequences ore longer thon ihose used in ihe pre-vious 2 steps. Throughout these sequences of moves,only o single top-corner cube (the one thot stod.s of FRT)

is ever more thon one turn owoy from its correct positionond orientotion, Should you gpt lost or moke c mistokeduring one of these sequences, simply stop ondreconstruct the T foce. Generolly, you will hove to rototeeither ihe F or R foce to return cubes to the top ond then

. repeot one of the sequences in step 2 lo return thewondering top-corner cube. Hoving done this, try ogoinstortirq ot step 3A.

Shorl cuts

l. It is rorely necessoryto drop FRto the Bfoce(step 3B). Simply ploce ond orieni thosecubes okeody on the B foce into their cor-reci positions. This will oulomoticolly droporcther edQp cube to the B foce,

2. (fxpe*) n mojor reduction in the number ofmoves required cqn be ochieved by com-bining step 2 (top corners) ond step 3 (ver-ticol edges), You moy hove'noticed thotthe sequences in step 3 unrovel, ond thenportiolly repeot, those of step 2 Try to f(7ureout how to combirre the 2 stePs.

-44*

41

STEP 4: BCTTOM CORNERS(BFL, BFR, BLP, BPR)

BOTTOM FACE

The nex.f slep is fo plcce oncj orient the 4 corner cubeson the B foce. This is done by first plocing ihe cubes ondthen orienting thern, These 4 cubes ore not ploced inde-pendently bui os q set oll of once. To cornplete this step,you must follow the instructions of steps 4A-4E just once.

4A.First, it is necessory to rotote the B fcce until thelorgesi nurnber of bottom-corner cubes are prop-erly positioned with no concern for orientotion,lgnore the edge cubes on the B foce for now.Rotote the B foce until you get either 2 or all 4 of thebottom-corner cubes conectly positiored. lt willolwoys be possible to position conectly either 2 oroll 4 of the bottom-corner cubes by just rototing theB foce, ff oll 4 ore correctly positioned, proceed iostep 4D. lf 2 ore correctly positioned. the 2 fhot re-moin out of doce will be either on odjocent corr€rsor opposite (drogonol) corners. lf they ore on.odjo-cent corners, do step 48. lf they ore on opposiie(diogonal) corners, do step 4C,

42

ADJACENTEXCHANGE

DIAGONALEXCHANGE

48. tt the 2 out-of-ploce corner cubes ore odjocent, dothe following sequence, Hold the cube so thot the' cubes thot must be exchonged ore BFL ond BFR.

"Exchsnge BFL qnd BFR:R- B- R+ F+ B+ F- .R- B+ R+ 82

Now proceed to step 4D.

4{C.tt the 2 out-of-ploce corner cubes ore'diogonol, dothe following sequence, Hold the cube so thot thecubes thot must be exchonged ore BFL ond BPR.

"Exchonge BFL qnd BPR:R- B- R+ F+ 82 F- R- B+ R+ B+

4D.me 4 bottom-corner cubes ore now oll properlypositioned. Look of the B foce ond hold the cube sothot the color pottern on the.bottom corner cubesmotches one of the 7 potterns BCI-BC7. Only thebottom color is indicoted in block on the potternsBCI-BC7. The oniy other possibility is thot oll oreoriented correctiy. Remember to ignore the

_ bottom-edge cubes for now, lf necessory, turn theentire cube in your hond untilthe pcttern motches. one of the 7.

. This matching of coior potterns is done todetermine which will be your F foce for the next se-quence. Moke sure the T foce is os olwoys ond pro-ceed io step 4E.

43

4E. Perform the following sequence.

"Orienl bollom-corner cubes:R. B- R+ B- R- 82 R+ 82

'f+. i*lf the 4 bottom-corner cubes ore not correctly ori-ented ofter performing this sequence, go bock tostep 4D, You moy hove to perforrn the sequence instep 4E os mony os o tololof 3 times to orient thebottom-corner cubes,

Error eorreclionBefore doing the orientotion sequence in step 4E, it isnecessory to hold the cube correctly so thot the T foce is

os clwoys ond the F foce is os indicoted in the drowingsof the 7 potlerns BCI-BC7. Should you hold the cube in-correctly ond do ihis sequence, you will merely get bocko differeni pot.tern of the 7 possible. Should this hoppen,simpiy rnotch the potlern you do get to one of tl^re 7 ondlry ogoin by repeoting step 4D.

lf you moke o mistoke when posiiioning or orienting thebottom-corner cubes, it is possible you moy end up withone of the verticol-edge cubes misploced. Should fhishcppen, you will hove to go back to step 3, correct theerror uging one of the sequences in thot step, clnd thenrelurn to step 4,

Ye t\a i)

Fr{'4gr-.lf B I

kI i-wc I{ J -_---)\r,; /

----+-+

it ir,..jc

rF--: L,.u"

v

BC7THE SEVEN POSSIBLE COLOI? PATTERNS OI..i THE BOTTOM FACE'

REMEMBER IO IGNORE THE C'JLORS OF THE BOTTOM EDGE CUBES'

44

^\.I

BCI

PBC6

i\L)

45

Short euls

,'-r 46

l. Use the reverse of the orientotion sequence.

Orient bottomcorner cubes (reverse):82 R- 82 R+ B+ R- B+ R+

whenever the BC2 potiern occurs. Use fheforword seguence given obove wheneverthe BC1 pottern occurs. This will usuollyeliminote 8 moves from the overollsolution.

2. This shorter sequence exchonges twodiogonol bottom-corner cubes os requiredin step 4C. lt does not motter which foce is

the F foce, Only the T ond B foces must re-moin the some os olwoYs. Use this os oreplocement for the sequence in step 4D,

F_ B- R- B+ R+ F+

STEP 5: BOTTOMI EDGES (BF, BL BF, BR)

BOTTOM FACE

The finol siep is io ploce ond orient the 4 botfom-edgecubes. First check to see how mqnv of these 4 cubes crealready conectty psitA&gwitteut rqard to orienta-iion), At this point. there wilt.pp either 4,.l, or none of thesebotlom-edge cubes conectly' pSicsitioned.

lf none ore correctly positioned,go to step 5A.

lf I is correctly positioned, go to step 58.

lf 4 ore correctly positioned, go to step 5C,

The sequences (L- R+ ) ond (L+ R-) ore done repeot-edly in this step, They ore put into parentheses for cloritv.

5A. Oo the following sequence (oll 11 moves). lt does notmatter ho',v the cube is held crs long os the T ond Bfoces remoin os before

"(L- R+) F+ (L+ n-) 82(t- R+) F+ (L+ R-)

p€,''.\+lier+=;r--,-

47

Now there will be exoctly one of the bottom-edgecubes properly positioned, olthough the orientotionmoy be incorrect. At this point, go to step 58.

58. Hotc the eube so thot the properly positionedbottom-efte cube is in position BF, Then cjo thefollowing sequence (oll 11 moves).

(L+ R-) 82(L+ R-)

if it is BEl, do step 5D,

lf it is BE2, dc step 5E.

lf it is BE3, do step 5F.

P+) F+R+) F+

This sequence is ihe some os the one in step 5A. lfthe 4 bottom-edge cubes ore stiil not conectlypositioned. cja the sequence ogoin with the prop-erly positioneC cube in position BF, At this point, oiithe botiom-edge cubes wiil be conectly posi-

tioned. lf the cube is completed, gc lc step 5Gotherwise, g* to step 5C.

5C"ntt4 bottorn-edge cube-s ore cor;'ectiy pcsitioned,ond the B face will show the bottcm color in one ofthe three potterns BEI-BE3, i{old the cube so thepottern motches. if necessory, iurn the entire cubein ycur hond uniii rhe pottern you hcve motchesone of the three. Be sud$She T foce is the some osolwoys ondthe f rcdisS indiccted inthe potternsBC]-BC3, '-*.. d

f*'jt:

i-lr--!1l

,-r l-i(

l

,

jr=-

I

G{"*t

'b

!

t="-:€f'***r-a*s-.-

49

5f), Do tlre fosowirg seqer€e to cornplete the puzzb

R-) 82 (L- R+)R+) F2 (L+ R-)

"Allernqtive method br step 5tt is possible to complete ihe cube from oll3 potterns (8E1.

BEZ BE3) using only the sequences in steps 5F ond 58' lfyou get pottern BElor BE2, simply perform the sequencesin step 5F ond then 58 os directed, moking sure only thotthe T ond B foces remoin ihe some, This will give bockpottern BE3, which is then completed using step 5F.

eo74{}}

(oll18 moves)'(L- R+) F2 (L+(L+ R-) 82 (L-

I'Jow go to step 5G'

F+B-

.!R-) B- (L- n+) F-R+i F2 (t+ R-)

I.tJI

II*-dIi

5E. Oo the fdkrwirg seqrrnce to cornplete the puzzle- -' (Jt go ilveO. FoojG cuoe so tnot me 2 conectlv

#;;i-d;#;*ds; Cuoes ore in Positions BL

ond BR.

(L- R+) F+ (L+ R-) B+

il* n+i r+ (L+ R-) B+

ir- n+i rz G+ R-) B+

il- n+ i r+ (r-+ R-) B+

cr- n+) F+ (L+ R-) 82

This is o long sequence' but note thot you ore

or*"vtJutnitb tne'F ond B foces in the some direc-

tion ibbct<wise). Go to steP 5G'

5F, oo the following sequenc€ (oll'17 mov-es) Hold the-' ' ;ne;o thot thb BF'onu BR bre correctly oriented'

i ,..i

"(L- R+) F+ (L+

il,+ R-) B- (t-

Then go bock ond do step 58' ofter which the

puzzte witt be comPleted'

SG.fett everyone within shouting.distonce ond reword---Vouo"ft *itn o trip to the refrigerotor'

W,Y'"

5l

Error correclionThe net resull of the sequence

(L* R+) F (+, -,or2)(L+ R-)

is to move one of the top-edge cubes to the B foce ondreploce it with one of the botfom-edge cubes, Loter on,the top-edge cube is returned to its proper position ondorientotion. Should you moke o mistoke or jusi get lostduring one of these lengthy seguences, simply return thewondering top-edge cube to its correct position-bydoing the following:

l. Hold ihe cube so thot the wondering iop-edge cubebelongs in the FT position,

2. Move the wondering top-edge cube to position BR

by rototing the B foce.

3. Oo the sequence (L- R+ ) F- (L+ R-)This will put the top-edge cube into its correct posi-tion on the T foce, However, the orientotion moy bewrong. Should this hoppen, do the followingsequence:

Orient top-edge cube:(L- R+) F2 (L+ R-) B+ (L- R+) F- (L+ R-)

Allthe sequences in step 5, when completed,leove oll 8corner cubes,4 verticol-edge cubes, ond 3 top-edgecubes unmolested, so o serious error is unlikely, Shouldsomething disostrous occur, simply see how much of thecomdeted portion of the cube remoins correct ond gobock to the oppropriote previous step to correct onyerrors.

Short cuts

\

:,I

L Use fhe reverse of the sequence in step 58.

Remember thot bottom-edge cube BF

must be correctly positioned,

(L- R+) F- (L+ R-) 82(L- R+) F- (L+ R*)

Determine the chonges of the bottom-edge cubes thot these sequences couse.Figure out when to use the forword se-quence ond when to use the reverse se-quence. The correct choice will ustiollyeliminote ll moves,

2. (Experl) lt is possible to reduce significontlythe number of moves reQuired to occom-plish step 5 by positioning ond orienting thebottom-edge cubes of the some tirne. Try

to design sequences of moves similor tothose in steps 5A oncl5F fhot permute thebottom-edge cubes in different woys. Thenleorn to recognize the orrongements of thebottomedge cubes thot require thesenew sequences of moves, You wili likelyhov-e to recognize more thcn just threepofter,rs @l-BC3) but will comBlete thegfu ln s(2rrtfrcontly fewer moves, Even oit|s bte stoge, it is still possible to ploce ondcr€nt 3're of the bottom-edge cubes inde-percnfi\ cf tfle other three, One oP-

Fr# *c rrycvrng step 5 is to ccrrectlypdg crri srent I botiorn+dge cube inlfe ffisf h'glf cnd th€{r dect.with the re-rrriTrg3ooset

50

AFTENWORDlcon usuolly solve rondom cube problems by using thissolution with the simpler short cuts provided in obout 2Yz

minutes. lfind o consideroble omount of time is spent inlocoting cubes ond oligning the foces so thoi the nextmove con be mode. The stiffness of the cube is qdecisive foctor in time triqls.

As wos pointed out in the lntroduction, this solution doesnot involve the fewest number of moves possible, Never-theless, by using oll the moves provided, including the"expert" short cuts, I con overoge less thon IOO movesfor solution of o rondom cube problem, olthoughoccosionolly more thon IOO moves ore required. To

ochieve this reduction,lhove to combine steps 2 ond 3,

but the other steps remoin the some. There is nothingsocred obout breoking up the solution into these 5 steps,ond o betler solution moy well use o different meihod.

An interesting postime (or obsession) is to try to find bet-ter solutions for this foscinoting puzzle. lt is octuolly pos-sible to rotionolly design sequences of moves thot hovedesired overolleffects, Try the sequence:

(L- R+) F2 (L+ R-) 82

This tokes ihe cube thot storts ouf in the FT position to theBP position, ihe cube in BP to BF, ond the cube in BF to FT, ltis best to try this on o solved cube to see the overoll ef-fect. Now, on o solved cube, do the foltowing 2-movesequence.

R2 T+

=his hos the effeei of lcking a cube frcm BR to FT, Now, on,'he some cube, do the sequence:

(L- R+ ) F2 (L+ t?-) 82

Thls is the scme os the one given obove. Then "undo" thefirsi 2 moves:

T -n4t- taL

.rhe overoll effect is BP to BF to BR to BP. By preceding the&r^nove sequence wiih various moves ond following it*iith the exocf reverse of those rnoves, you ccn choose?c exchonge ony 3 edge cubes without disturbing theother 9 edge cubes ond oll 8 corner cubes. Using tricksike this, it is possible to move the cubes oround olmost otrr#.

A recl chollenge is to develop o shorler solution thot is

eso cbor, simBle, ond error toleront,

noppy curbitgl