rubiks cube 4x4x4 solver

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Rubik’s Revenge Solution Hints Booklet Revenge - The Ultimate Challenge 2 Meet Your Revenge 3 Twisting Hints 5 General Hints 8 Notation System 12 Revenge Sequences 19 Solving Rubik’s Revenge 28 More Revenge 33 1

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Page 1: Rubiks Cube 4x4x4 Solver

Rubik’s RevengeSolution Hints Booklet

Revenge - The Ultimate Challenge 2

Meet Your Revenge 3

Twisting Hints 5

General Hints 8

Notation System 12

Revenge Sequences 19

Solving Rubik’s Revenge 28

More Revenge 33

1

Page 2: Rubiks Cube 4x4x4 Solver

2 3

Revenge - The Ultimate Challenge

RUBIK’S Revenge is the big brother of the bestselling, original RUBIK’S Cube. Some of the movesthat you might know that work on the original Cubealso work on Rubik’s Revenge - but be warned: thesimilarity stops there.

Rubik’s Revenge presents a completely newchallenge. You must mix up the puzzle with a fewtwists and turns and then try to match up thepieces until each face is a single colour. However,you are advised to read the first few sections ofthis booklet first.

Try to solve the puzzle logically, but be careful. Bevery, very careful. Your success will depend onhow well you grapple with the totally unexpectedproblems you will meet.

With millions more combinations than the original,Cube plus its own special devilry, you should bewary of Rubik’s Revenge - the Ultimate Challenge.

Meet Your Revenge

RUBIK’S Revenge has 6 faces. Each face will be asingle solid colour when the puzzle is solved.

The puzzle has 12 different layers and each canbe turned independently of the others.

� Front Layer

� Back LayerLeft

Layer �

Mid-Left Layer �

Right �

Top Layer �

Mid-Top Layer �Bottom Layer �

� Mid-Back Layer

Mid-Bottom Layer �

Mid-Right Layer �

� Mid-Front Layer

TOP

FRONT RIGHT

Page 3: Rubiks Cube 4x4x4 Solver

4 5

Meet Your Revenge

Revenge is made of 56 smaller cube pieces.24 have a single colour - these are Face Pieces,24 have two colours - these are Edge Pieces;and 8 have three colours - these are CornerPieces.

Twisting Hints

There are two kinds of twist that can be given toany layer: a quarter twist and a half twist.

A quarter twist rotates one layer of the puzzle 90ºclockwise or anticlockwise. A half twist rotates onelayer 180º. (Twisting a layer through three quar-ters is the same as twisting it one in the oppositedirection.)

`

CornerPiece

EdgePiece

FacePiece

When the puzzle is solved, the Yellow face isalways opposite the White face; Blue is oppositeGreen, and Red is opposite Orange.

Also, when the Yellow face is on top, Blue is atthe front when Red is on the right, as in the dia-gram above.

TOP

FRONT RIGHT Right Layer:Quarter twistclockwiseRight Layer:

Quarter twistanticlockwise

Right Layer:Half twist

Page 4: Rubiks Cube 4x4x4 Solver

6 7

Twisting Hints

Think of the orientation. For example, moving theback right corner piece with a half twist will put itdiagonally opposite and upside down.

Twisting Hints

Whenever you move a piece, performing themoves you made backwards will return the puzzleto its original position.

TOP

FRONT RIGHT Right Layer:Half twist

If the same piece were instead moved by twoquarter twists of two different layers, it would endin the same position but in a different orientation.

Bottom Layer:Quarter twistanticlockwise

Front Layer:Quarter twistanticlockwise

As an exercise in twisting,try this: from the solvedposition, twist two adjacentlayers at a time (as thoughthe cube were 2x2), and tryto get each face with four2x2 blocks of four differentcolours as shown here.

Now try to put the puzzleback into the solved position. This is the same astrying to solve the Mini-Cube or just the corners ofthe Revenge.

Don’t worry if your Revenge gets muddled up,there are some General Hints in the next section.

Page 5: Rubiks Cube 4x4x4 Solver

8 9

General Hints

If you haven’t jumbled your Revenge up, now isthe time to start.

Then, try to solve the puzzle logically.

Unlike Rubik’s Cube, the face pieces do not deter-mine which face is which colour. In fact, there arefour face pieces of each colour. It is best to startfrom a corner piece.

General Hints

Now that you can see which pieces must go where,try to build up on your chosen corner piece. You cando this in several ways. For example:

Layer by Layer:

TOP

FRONT RIGHT

Turn the puzzle so that yourchosen corner is on the toplayer. In the example here,the Red/Yellow/Blue piecehas been used. This pieceshows what colour the facesmust be. Remember, Blue isopposite Green; Red isopposite Orange; andYellow is opposite White.

Step 1 Step 2

Step 3 Step 4

Page 6: Rubiks Cube 4x4x4 Solver

10 11

General Hints

Edges; Corners, and Faces:

General Hints

Experiment with different sequences of twists tofind out what they do. Try to find some that movepieces you have already positioned to one sideand then put them back in place. You will oftenfind that other pieces yet to be placed have eithermoved about or been reorientated. You shouldmake a note of any effects that look useful so thatyou can repeat them to achieve a desired result.

However, to do this you must use a system torecord your moves and the effects. Also, you willneed to put numbered or lettered stickers ontoyour puzzle to differentiate between identicalpieces. (For example, Blue face pieces could benumbered 1 to 4 and Blue/Red edge piecestagged A and B. This makes it easier to see whathas moved where.

A system for recording your sequences is given inthe next section.

Step 1 Step 2

Step 3 Step 4

Some methods will prove more difficult than oth-ers, so try different ways. (There is one thatavoids the problems the others may encounter.)Whichever approach you use, you will needdifferent sequences: some which just affect facepieces; some that just affect edge pieces; andsome that just affect corner pieces.

Page 7: Rubiks Cube 4x4x4 Solver

Notation System

The layers of Rubik’s Revenge are as labelledhere.

� Front Layer

� Back LayerLeft

Layer �

Mid-Left Layer �

Right �

Top Layer �

Mid-Top Layer �Bottom Layer �

�Mid-Back Layer

Mid-Bottom Layer �

Mid-Right Layer �

� Mid-Front Layer

TOP

FRONT RIGHT

The front face is the one that is facing you whenyou start the sequence. Keep that face towardsyou throughout the sequence.

Notation System

Remember to look for sequences that do notdisturb pieces already positioned: those piecesshould end up where they started. Only recordsequences that do this.

Movement of a layer is recorded by the layer’sname and an arrow. The arrow gives the directionthat the front or top edge of that layer is movedone quarter turn. Thus, for example:

Notation Indicates:Front� Front layer one quarter twist to left.Back� Back layer one quarter twist to right.Top� Top layer one quarter twist to left.Bottom� Bottom layer one quarter twist to left.Left� Left layer one quarter twist down.Right� Right layer one quarter twist up.Mid-Left� Mid-Left layer one quarter twist down.Mid-Back� Mid-Back layer a quarter twist to left.

12 13

Page 8: Rubiks Cube 4x4x4 Solver

Notation System

Remember, the direction relates to the visibleedge of that layer at the top or front.

With a half-twist, direction is irrelevant, so this isshown by replacing the arrow with a 2. So, Front2means that the front layer is rotated a half-twist.

You may want to twist two layers together. Thisshould be recorded as, say:

Bottom+Mid-Bottom�

You may find it tricky to twist a middle layer. Inpractice, it’s easier to twist it with the adjacent facelayer and then turn the face layer back.

There is a reason for the way the puzzle isviewed. This enables you to see how the piecesalready positioned are moved out of the way andwhere they go to. If you can see this clearly, youwill find it much easier to remember the sequence.

14 15

Notation System

To note the start and finish positions, so that youcan see what has happened after a sequence ofmoves, copy and use the diagrams below.

This is the one used in this booklet. It representsthe view of the bottom layer (and a false perspec-tive of the sides) you would have if you tilt thepuzzle away from you.

Start Position End Position

SEQUENCE:

Page 9: Rubiks Cube 4x4x4 Solver

Notation System

Just record the effect that is relevant. For example,suppose you find a sequence that moves one edgepiece from the bottom layer to the mid-top layerwhile leaving the pieces in the top layer and theother edge pieces in the mid-top layer unchanged.This is the only important effect. You do not need tonote what happens to the other pieces on thebottom and mid-bottom layers. All you need toknow is the start position of the piece that ended inthe mid-top layer.

For example, your start and end position shouldsimply be noted as here (along with your sequenceof moves).

Start Position End Position

*

**

*

**(Asterisked pieces remain unmoved.)

16 17

Notation System

For each sequence that you find, there will also bea Reverse, a Mirror, and a Reverse Mirror.

Suppose you have found a sequence that reads:

Mid-Left�; Bottom�; Mid-Left�; Bottom2;Mid-Left�; Bottom�; Mid-Left�.

The Reverse is the sequence in reverse order withthe direction of arrows also reversed, as here:

Mid-Left�; Bottom�; MId-Left�; Bottom2;Mid-Left�; Bottom�; Mid-Left�.

The start position of the Reverse is the end posi-tion of the original sequence, and the Reverseends with the start position of the original. So, ifyou perform a sequence and then wish to put thepuzzle back as it was, simply do the Reverse ofthe one you did to restore the original position.

Page 10: Rubiks Cube 4x4x4 Solver

Notation System

A MIrror sequence is a left-right reflection of theoriginal. This swaps left and right without changingthe arrows and reverses all other arrows TheMirror of the previous sequence would be:

Mid-Right�; Bottom�; Mid-Right�; Bottom2;Mid-Right�; Bottom�; Mid-Right�.

Start and end positions are reflections of those forthe original sequence. For example, the diagramshere are the reflections of those on page 16.

End PositionStart Position

18 19

**

Whenever you find a useful sequence, make sureyou also record these other versions. If you havetrouble finding your own sequences, some usefulones are given in the next section.

Revenge Sequences

This section contains some general sequences tocover many situations. (There are other morespecific sequences for you to find.) The system ofnotation is as described in the previous section.

The start and end positions show the bottomface. (That is, the view you would have if you tiltthe puzzle away from you.) Start and end positionsfor the Reverse and Mirror versions have beenomitted for reasons of space.

Always hold the puzzle so that the piece you wishto move is in the appropriate start position.

Asterisked pieces remain unmoved as do all theother pieces of the puzzle.

The relevant pieces to be moved are hatched toavoid confusion with the colours you might beplacing.

* * * *

Page 11: Rubiks Cube 4x4x4 Solver

20 21

Start Position End Position123123123123123123123123

123123123123123123123

12345123451234512345

123123123123123123123123

123456712345671234567

*

**

* ***

123451234512345123451234512345

123456781234567812345678

123123123123123123

123456712345671234567

*

**

* ***

123456712345671234567

Revenge Sequences

Three-Corner ShuttleThis shuttles a triangle of corner pieces one placeclockwise around the bottom layer.

Left�; Bottom�; Left�; Front�; Bottom�;Front�; Left�; Bottom�; Left�; Bottom�.

ReverseBottom�; Left�; Bottom�; Left�; Front�;Bottom�; Front�; Left�; Bottom�; Left�.

MirrorRight�; Bottom�; Right�; Front�; Bottom�;Front�; Right�; Bottom�; Right�; Bottom�.

Reverse MirrorBottom�; Right�; Bottom�; Right�; Front�;Bottom�; Front�; Right�; Bottom�; Right�.

1234123412341234

Start Position End Position123123123123123123123123

123451234512345123451234512345

123456781234567812345678

*

**

123123123123123123

123123123123123123123123

123456123456123456123456123456123456

123123123123123123123

*

**

123456781234567812345678

Revenge Sequences

Three-Corner FlipperThis flips three corner pieces on the bottom layerwithout changing their position.

Right�; Bottom�; Right�; Bottom�; Right�;Bottom2; Right�; Bottom2.

ReverseBottom2; Right�; Bottom2; Right�; Bottom�;

Right�; Bottom�; Right�.

MirrorLeft�; Bottom�; Left�; Bottom�; Left�;

Bottom2; Left�; Bottom2.

Reverse MIrrorBottom2; Left�; Bottom2; Left�; Bottom�;

Left�; Bottom�; Left�.

Page 12: Rubiks Cube 4x4x4 Solver

Revenge Sequences

Low-Edge ShuttleBy shuttling a triangle of edge pieces clockwisearound the front layer, this moves an edge piecefrom the mid-bottom layer into the bottom layer.

Left�; Bottom�; Left�; Mid-Bottom�;Left�; Bottom�; Left�; Mid-Bottom�.

ReverseMid-Bottom�; Left�; Bottom�; Left�;Mid-Bottom�; Left�; Bottom�; Left�.

MirrorRight�; Bottom�; Right�; Mid-Bottom�;Right�; Bottom�; Right�; Mid-Bottom�.

Reverse MirrorMid-Bottom�; Right�; Bottom�; Right�;Mid-Bottom�; Right�; Bottom�; Right�.

22 23

Revenge Sequences

High-Edge ShuttleBy shuttling a triangle of edge pieces clockwisearound the front layer, this moves an edge piecefrom the mid-top layer into the bottom layer,

Left�; Bottom�; Left�; Mid-Top�;Left�; Bottom�; Left�; Mid-Top�.

ReverseMid-Top�; Left�; Bottom�; Left�;Mid-Top�; Left�; Bottom�; Left�.

MirrorRight�; Bottom�; Right�; Mid-Top�;Right�; Bottom�; Right�; Mid-Top�.

Reverse MirrorMid-Top�; Right�; Bottom�; Right�;Mid-Top�; Right�; Bottom�; Right�.

Start Position End Position123456781234567812345678

* ** ** *

* ** **

* ** *

1234512345

123456781234567812345678

123123123123123123123

* ** ** *

* ** **

* ** *

123456712345671234567

123123123123123123123123123

Start Position End Position123123123123123123123123123123

12121212121212

* ** ** *

***

*

* ** *

**

*123456712345671234567

1234567890123456789012345678901234567890

123456789123456789123456789123456789

* ** ** *

***

*

* ** *

**

*12345123451234512345

Page 13: Rubiks Cube 4x4x4 Solver

24 25

Revenge Sequences

Face-LifterThis shuttles three face pieces.

Mid-Left+Mid-Right�; Bottom�; Mid-Right�;Bottom�; Mid-Left�; Bottom�; Mid-Right�;

Bottom�; MId-Right�.123456781234567812345678

12341234123412341234

Start Position End Position

* *

* *

* * ** **

* ***

123456123456

123456123456123456123456123456123456

* *

* *

* * ** **

* ***

ReverseMid-Right�; Bottom�; Mid-Right�; Bottom�;Mid-Left�; Bottom�; Mid-Right�; Bottom�;

Mid-Left+MId-Right�.

MirrorMid-Left+Mid-Right�; Bottom�; Mid-Left�;Bottom�; Mid-Right�; Bottom�; Mid-Left�;

Bottom�; MId-Left�.

Reverse MirrorMid-Left�; Bottom�; Mid-Left�; Bottom�;

Mid-Right�; Bottom�; Mid-Left�; Bottom�;Mid-Left+MId-Right�.

Revenge Sequences

Mid-SwapperThis swaps two adjacent edge pieces in the frontmiddle layers.

Front2; Mid-Bottom�; Front2; Mid-Bottom2;Front2; Mid-Bottom�; Front2.

MirrorFront2; Mid-Bottom�; Front2; Mid-Bottom2;

Front2; Mid-Bottom�; Front2.

In both cases the reverse is the same as thesequence.

*

1234567123456712

12121212

123456781234567812345678

Start Position

* ** ** *

***

* ** *

**

*

1234123412341234123412341234123412341234

1234567890123456789012345678901234567890

123123123123123123123

Start Position

* ** ** *

***

* ** *

**

*

Page 14: Rubiks Cube 4x4x4 Solver

123123123123123123123123

123456123456

*

123123123123123123

Start Position

* ** ** *

***

* ** *

**

*

123456789123456789123456789

123123123123123123123123123

121212121212 *

123123123123123123123123123

123456789123456789123456789

End Position

* ** ** *

***

* ** *

**

*

123456781234567812345678

121212121212

* *

*

*

*

*

* *

* *

*

*

**

* *

Revenge Sequences

Mid-ShuttleThis shuttles a triangle of edge pieces clockwisearound the mid-bottom layer.

Back�; Bottom2;Left�; Bottom�; Left�; Mid-Bottom�;Left�; Bottom�; Left�; Mid-Bottom�;

Bottom2; Back�.

ReverseBack�; Bottom2;

Mid-Bottom�; Left�; Bottom�; Left�;Mid-Bottom�; Left�; Bottom�; Left�;

Bottom2; Back�.

Revenge SequencesRevenge SequencesRevenge SequencesRevenge SequencesRevenge Sequences

MirrorBack�; Bottom2;

Right�; Bottom�; Right�; Mid-Bottom�;Right�; Bottom�; Right�; Mid-Bottom�;

Bottom2; Back�.

Reverse MirrorBack�; Bottom2;

Mid-Bottom�; Right�; Bottom�; Right�;Mid-Bottom�; Right�; Bottom�; Right�;

Bottom2; Back�.

With this sequence (as with any that shuttles threepieces), performing it twice has the same effectas doing the Reverse once.

You should try and solve the puzzle for yourselfusing the sequences provided. They are all youneed - plus a little imagination. If you are stillhaving trouble, a full solution guide is given in thenext section.

26 27

Page 15: Rubiks Cube 4x4x4 Solver

Solving RUBIK’S Revenge

Once you start twisting, it’s easy to get Rubik’sRevenge completely muddled. Don’t worry - it canalways be put right from any state. The followingsteps will help you solve the puzzle.

Solving Rubik’s Revenge

28 29

TOP

FRONT RIGHT

1. Select any corner piece asyour starting corner. Turnthe puzzle so that this pieceis in the top face. It is auto-matically in the correctposition. (In our example,Yellow is the top face andBlue is the front.)

2. Find a second piece that’sa side-by-side match and twist it into place.

TOP

FRONT RIGHT

3. Position all edge and cor-ner pieces of the top face.If you have trouble, use thesequences. (The Three-Corner, High-Edge, andLow-Edge Shuttles can allbe used if you turn thepuzzle so that your top facebecomes the relevant facein the sequence diagrams.)

4. Position the face pieces ofthe top layer by using theFace-Lifter.

TOP

FRONT RIGHT

NB - Of two identically coloured edge pieces,only one can be placed in a particular positionwith the colours correctly orientated.

NB - When using the Face-Lifter, you may first need totwist faces to align thepieces to be moved. Notethese so you can reversethem afterwards.

Page 16: Rubiks Cube 4x4x4 Solver

Solving Rubik’s Revenge

30 31

Solving Rubik’s Revenge

TOP

FRONT RIGHT

5. Next, and most importantly, complete thebottom face.

6. Start by using the Three-Corner Shuttle tocorrectly position the corner pieces. If twoseem to be correctly placed, turn the layer soone of the other two is correctly placed. TheThree-Corner Shuttle will then position theother three. If the two that need to be swappedare diagonally oppo-site, you will need touse the Three-CornerShuttle twice.

7. Once the cornerpieces are in the rightpositions, use theThree-Corner Flipperto orientate themcorrectly.

TOP

FRONT RIGHT

8. Use the Low-Edge and/orHigh-Edge Shuttles todrop the edge pieces intotheir correct positions onthe bottom face. If a pieceyou want is already in thebottom face, use one ofthe shuttles to remove it.

9. Complete the bottom faceby using the Face-Lifter.

10. Use the Mid-Swapper tocorrectly position theedge pieces of the mid-top layer. If a piece youwant is already in thatlayer, use the swapper toremove it.)

TOP

FRONT RIGHT

Page 17: Rubiks Cube 4x4x4 Solver

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Solving Rubik’s Revenge

TOP

FRONT RIGHT

11. Turn the mid-bottomlayer so that only oneedge piece is correctlypositioned. Then usethe Mid-Shuttle tocorreclty position theother three. If twodiagonally oppositeedge pieces need to beswapped, you will needto use the shuttle twice.

12. Finally, complete thecentre faces by usingthe Face Lifter.

TOP

FRONT RIGHT

More Revenge

Once you’ve mastered the puzzle, there is morefun to be had.

Try solving the puzzle layer bylayer from the top down.There’s a fifty-fifty chanceyou’ll either solve it or reachthe position shown here.From this position, see if youcan find the shortest se-quence that will solve thepuzzle.

Other patterns can be made.For example, is it possible tomake all the faces a checker-board pattern?

Rubik’s Revenge isn’t overyet.