How to Solve a Rubik’s Cube Benjamin Popp

7/23/2019 How to Solve a Rubiks Cube Benjamin Popp

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How to Solve a Rubiks Cube 1 Benjamin Popp

A Guide for Beginners

Benjamin Popp

Benjamin Popp

HOW TO SOLVE A RUBIKS CUBE

AGUIDE FOR BEGINNERS


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Table of Contents

Introduction . . . . . . . . . . 3

Before you Begin . . . . . . . . . 4

Task I: Solving the Upper Layer . . . . . . 6

Task II: Solving the Middle Layer . . . . . . 10

Task III: Solving the Bottom Layer . . . . . . 11

Appendix A: Pattern Quick Reference . . . . . . 15

Appendix B: Extended Lower Layer Patterns . . . . . 16

Appendix C: Internet References . . . . . . . 18


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Introduction

This instruction set will help any beginner solve the Rubiks Cube. The Cube can be intimidating

to people who do not understand it, but it is easier to solve than it looks. With this guide and a

little practice you can solve the Rubiks Cube in less than five minutes.

The Cube will be solved in three basic tasks: solving the top layer, solving the middle layer, and

solving the bottom layer. The process of solving the Cube is the simplest when broken into

these three sections.

Things You Will Need

The Rubiks Cubeor other off-brand Cube puzzle.

This guide makes the most sense when you actually have a Cube available. If you

do not have a Cube with you, it might be a good idea to wait and try using thisguide once you have a Cube.

Time

The first time solving the Cube with this guide could take about an hour. Once

you are accustom to the notation and the general steps, solving the cube will

become a faster and more natural process.

This Guide

The first time through, this guide will be very helpful. The second time you

might only need the figures; Appendix A is a condensed solution set for the

middle and lower layers.

All notes and tips to help along the way

will appear in a box with a yellow

heading like this one.

Note:

Common problems are solved in boxes

with a blue header like this one.

What if something doesnt

work quite right?


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Before You Begin

Over the years, the Rubiks Cube solving community created

standard notation and words to talk about the Rubiks Cube.

This guide will use the standard notation as described below.

Cubie One of the miniature cubes in a Rubiks Cube

Center Cubie One of the six fixed centers with one visible

color (Figure i)

Corner Cubie One of the eight rotating cubies with three

visible colors (Figure ii)

Edge Cubie One of the twelve rotating cubies with two

visible colors (Figure iii)

Face One side of the cube; the White face is the

face with a White center, the Up face is the

face with the center directed upward, etc.

(Figure iv)

Layer All the cubies that are on a face; the upper

layer is the nine cubies with colors on the Up

face, the front layer is the nine cubies with

colors on the front face, etc.

Turn Moving the cube in your hands, but not

changing the cube in any way. Usually this will

keep the same face on top and change the

front and side faces.

Twist Changing a face with respect to the other

faces.

The six faces are defined as:

(U)p,

(D)own,

(L)eft,

(R)ight,

(F)ront, and

(B)ack

In this guide, all figures will appear with six sides, three of

which are seen as if mirrors were around the cube. The

three connected sides will always be the Up face, Front face,

and Right face. Cubies that are not important for a specific

step will appear in gray to simplify the figures.

Figure i: 6 Center Cubies

______________________

Figure ii: 8 Corner Cubies

______________________

Figure iii: 12 Edge Cubies


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Use the pattern from the

Figure

During certain steps you will be asked to

perform a pattern in a Figure. This patternwill always be found directly below its

Figure and is written in parenthesis. A

capital letter means to twist a face

clockwise; a capital letter with an

apostrophe () means to twist that face

counterclockwise; a capital letter with the

number two (2) after it means twist that

face twice.

For example:

( U F R2 )

The above translates to twisting the Up face

clockwise, the Front face counterclockwise,

and the Right face twice.

Figure iv: The Six Faces

Twisting a face does not change the

colors on that face; it changes the

colors on the faces around it.

Note:

Look directly at a face and imagine a

clock on it, then twist that face in the

direction the hands of the clock wouldmove. Notice that this means that if

you are looking at the Front face of

the Cube, the Up face clockwise and

Down face clockwise appear to be

opposite directions.

Which way is clockwise

for a face?


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Task I: Solving the Upper Layer

If you have not scrambled your Cube, do so now. Before you begin this task your Cube must be

in total disarray. It will not stay scrambled very long; soon your Cube will have all of the White

face solved and half of the Red, Blue, Orange, and Green faces solved. Also make sure you haveread the Before You Begin section and you understand the basic Rubiks Cube vocabulary.

1.

Turn the Cube so the white face is the Up face.

The White Cross

2. Find the white-red edge cubie.

3. If that cubie is in the upper layer the lower layer, turn

the Cube until the cubie on the Front face and twist

the Front face either direction. This places the cubie

in the middle layer.

4.

Turn the Cube so the cubie is in the Front and Right

sides.

5. If the cubie has white on the Front face, twist the

Right face clockwise (Figure 1.5A). If the cubie has

white on the Right face, twist the Front face

counterclockwise (Figure 1.5B).

Figure 1.5A

( R )

______________________

Figure 1.5B

( F )

You can actually start with any face Up

you want, but this guide is easier to

understand if you solve White first.

Note:

Most modern Rubiks Cubes have White opposite Yellow, Red opposite

Orange, and Green opposite Blue. If your colors are different, you can still

use this guide; just look at the introduction section and decide which of

your colors is which based on the center cubies.

My colors are laid out different from yours!


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6. Repeat steps 2-5 for the white-green

edge cubie; before step 5, twist the

Up face so the green cubie will be

placed next to the red cubie (Figure

1.6).

7. Repeat steps 2-5 for the white-

orange edge cubie, placing it beside

the white-green cubie (Figure 1.7).

8. Repeat steps 2-5 for the white-blue

edge cubie, placing it beside the

white-red cubie (Figure 1.8).

9. Twist the Up face to align the four

white edge cubies with the four sidecenter cubies (Figure 1.9).

Figure 1.6

Figure 1.8

Figure 1.7

Figure 1.9

If you have trouble getting white edges

into the upper layer correctly, just try all

the possibilities. If a twist produces an

undesired effect, undo that twist and try

twisting the Up face before continuing.

Note:

Some of your white edges are in the

wrong place. See the note above.

My centers line up

wrong in step 9!


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The White Corners

10.Choose two adjacent sides, such as red and blue.

Find a corner cubie with those colors and white. If it

is in the upper layer, turn the Cube so the cubie is in

the Front-Right-Up corner and use the pattern in

Figure 1.10 to move it to the bottom layer.

11.Twist the Down face to place the cubie directly

beneath its desired location.

12.Turn the Cube so the cubie is in the Front-Right-Down

corner and perform the pattern in Figure 1.12

continuously until the piece is correctly positioned.

13.

Repeat steps 10-12 for each of the four white corner

pieces.

Figure 1.10

( R D R )

______________________

Figure 1.12

( D R D R )

Do NOT choose a white corner cubiethat is already in place with white on

the Up face in step 10. You know a

cubie is in place when its colors match

the centers around it.

Note:

Those four twists will get the piece where it needs to go inthe direction it needs to be, but you might need to use the

pattern up to five times before the piece is correct. Also

make sure you are twisting the faces the right way; clockwise

for the Down face is opposite of clockwise for the Up face.

The pattern in Figure 11 was unhelpful


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14.Double check to make sure the Cube

looks like the Figure 1.14 before

moving on.

When you made it this far, take a deep

breath and relax a little; you just finished

one third of the Rubiks Cube! That is

farther than most people can get.

If you have time, go ahead and mix up the

Cube and solve the first layer again. Take

this opportunity to become comfortable

with how the cubies move together; the

more you understand the Cube, the easier it

is to work through the next two layers. Try

to understand how the patterns listed in

Figures 1.10 and 1.11 work instead of just

memorizing them; it will make Cube solving

more natural and less mechanical.

Figure 1.14

The upper layer completed

The method detailed here is just one

of many ways to solve the first layer.

If you want to solve the Cube for

speed, solving the upper layer shouldbecome natural so you can focus on

the parts that lie ahead.

Note:


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Task II: Solving the Middle Layer

This layer involves more complex patterns

than the upper layer, but also only involves

four cubies. From this point on, be carefulapplying the patterns; messing up a pattern

could force you back to solving the upper

layer.

1. Find an edge cubie in the bottom

layer with no yellow side.

2. Twist the Down face so the cubies

side color is under the center of the

same color.

3.

Look at the color on the bottom of

the cubie to decide if the cubie

should go up and left or up and

right.

4. Perform the pattern in Figure 2.4A

to move the cubie up and right, or

perform the pattern in Figure 2.4B

to move the cubie up and left.

5. Repeat steps 1-4 for each of the four

middle layer edge cubies.

You should now have at least six colors

correct on the four side faces as well as the

whole white face. Take another deep

breath; you will soon conquer the Rubiks

Cube.

Figure 2.4A

( D R D R D F D F )

_________________________

Figure 2.4B

( D F D F D R D R )

The middle layer is the eight cubies

between the upper and the lower

layer, NOT the eight cubies between

the front layer and the back layer or

the right layer and the left layer.

Note:

First make sure you are looking at the edges, not the corners. Use one of the patters in

Figures 2.4A and 2.4B to push a yellow edge cubie into the middle layer. This will pull a

cubie you need back to the bottom layer where you can apply one of the patterns again.

All the edges in the bottom layer have yellow sides!


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Task III: The Lower Layer

The bottom layer is the most reliant on

patterns; this is because you must be

careful not to ruin your work from the firsttwo layers while fixing the third layer.

1.

Turn the entire cube over so the

yellow face is the Up face and the

white face is the Down face.

Orienting the Yellow Cross

2. If you can turn the Cube to make it

look like Figure 3.2, skip to step 4.

3. Apply the pattern from Figure 3.2 to

the Cube. The front face color is

unimportant. Return to step 2.

4. Turn the Cube to make it look like

Figure 3.2 and aply the pattern from

Figure 3.2.

5. If you do not have the yellow cross

(Figure 3.5), return to step 2.

Figure 3.2

( F U R U R F )

Figure 3.5

The patterns used to solve the bottom layer are

freely available online from many websites and

are considered public domain. Appendix C lists

the website of Lars Petrus, the only known human

creator of some of these patterns.

Note:


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Positioning the Yellow Corners

6. Choose a color from one of the four

sides: red, green, blue, or orange.

Make sure there are two yellow

corner cubies of the chosen color in

the same side layer. For example, inFigure 3.8, both yellow-green corner

cubies are on the right layer.

7. Twist the Up face to allign those two

cubies with the center that shares

their color.

8. If those two cubies need to switch

places, turn the Cube so both cubies

are on the Right face, then use thepattern in Figure 3.8.

9. Repeat steps 6 through 8 for the

color on the opposite side of the

Cube. For example, if you chose

green first, repeat the steps for blue.

Figure 3.8

( L U R U L U R U2 )

The purpose of the next section is to get all the yellow corner cubies between the

center cubies with the same colors. For example, you want the fellow-green-orange

cubie between the yellow, green, and orange centers. It is not important for yellow to

face up on all of the corner cubies; just get the corners between the right centers.

Note:


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Finishing the Yellow Face

10.If the yellow face is solid, skip to

step 13. If the yellow face has

exactly one yellow corner cubie

facing up, skip to step 12.Otherwise, turn the cube so the

cubie in the up-front-left corner

does NOT have fellow facing up.

11.Use the pattern in Figure 3.11, then

return to step 10 if the Cube does

not look like either configuration in

Figure 3.11.

12.

Turn the Cube so the cubie in theup-front-left corner has yellow

facing up and perform the attern in

Figure 3.11 until the fellow face is

solid (you may have to use the

pattern twice).

13.Twist the Up face to align all the

corner cubies and make sure the

colors line up with the colors in theother two layers. If some corner

cubies have the wrong colors on

their sides, you made a mistake

while placing the corners; return to

step 6.

Figure 3.11

Configuration A

Configuration B

( R U R U R U2 R U2 )

The pattern in Figure 3.11 rotates three corner cubies at a time and can be difficult to

use. Due to this complexity, there is a little guess-and-check in the next section. If you

have trouble passing this step, Appendix B lists patterns for all possible configurationsfor the yellow face. Go directly to step 13 if you use one of those patterns instead.

Note:


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Finishing the Side Faces

14.If one of the four side faces is

solved, turn the Cube to make the

side face the Left face.

15.Use the pattern in Figure 3.14, then

return to step 14 if necessary. You

might have to do this up to three

times.

Congratulations! You just solved the

Rubiks Cube. Now that you understand the

process, you might try doing it again using

just Appendix A. If youre interested in

learning to solve the Cube faster, startworking with Appendix B for an extended

set of lower layer patterns or Appendix C

for internet references.

Figure 3.14

( R2 U F B R2 F B U R2 )

Appendix B lists more patterns for

solving the bottom layer. It can be

solved using only these four; however,

the more cases you remember, the

faster you can solve the cube.

Note:


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Appendix A: Pattern Quick Reference

( D R D R D F D F )

( F U R U R F )

( R U R U R U2 R U2 )

( D F D F D R D R )

( L U R U L U R U2)

( R2 U F B R2 F B U R2 )


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Appendix B: Extended Lower Layer Patterns

Yellow Face Patterns

V - Fix

F U R U R F

Line - Fix

F R U R U F

sune

R U R U R U2 R

cosune

R U R U R U2 R

double sune

R U R U R U R U R U2 R

anti-cosune anti-sune

R U2 R U R U R2 U2 R U R U R

sune cosune

R U R U R U2 R2 U R U R U2 R

bruno

R U2 R2 U R2 U R2 U2 R

triple sune

R U R U R U R U R U R U R U2 R


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Yellow Edge Patterns

Clockwise 3-Spin

R2 U F B R2 F B U R2

Reverse Pair Switch

R2 U F B R2 F B U R2

Counterclockwise 3-Spin

U R2 U2 R2 U2 R2 U R2 U2 R2 U2 R2

Adjacent Pair Switch

R U R U R U R U R U R U R2 U R U2


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Appendix C: Internet References

http://www.cubestation.co.uk/cs2/index.php?page=3x3x3/cfop/f2l/f2l

Dans Cube Station provides information about solving the Rubiks Cube using the F2L, or First-

2-Layers method. Instead of solving the cube layer by layer, the F2L solves the cube by fixing

the first two layers at the same time. It can be much faster than the method listed in this

document. However, there are also many more patterns to remember.

http://lar5.com/cube/

The website above explains the Petrus method for solving the Rubiks Cube, invented by Lars

Petrus. While fundamentally different from the method outlined here (Petrus begins by

creating a 2x2 Cube and expands it), the last section of the solution is very similar. Petrus alsoinvented the Sune pattern used in this document and the Niklas pattern which appears in

Figure 3.4.

http://www.geocities.com/rubiks_galaxia/PLL.html

The Permutation Last Layer is a system for speeding up the lower layer by adding more patterns

to move all the lower layer cubies at the same time. With this system, you would skip step 4-6

of the lower layer and just solve the face; then use one of the patterns listed on the web page

above to move all the cubies to their proper positions, solving the entire last layer in only threesteps.
http://www.cubestation.co.uk/cs2/index.php?page=3x3x3/cfop/f2l/f2lhttp://www.cubestation.co.uk/cs2/index.php?page=3x3x3/cfop/f2l/f2lhttp://lar5.com/cube/http://lar5.com/cube/http://www.geocities.com/rubiks_galaxia/PLL.htmlhttp://www.geocities.com/rubiks_galaxia/PLL.htmlhttp://www.geocities.com/rubiks_galaxia/PLL.htmlhttp://lar5.com/cube/http://www.cubestation.co.uk/cs2/index.php?page=3x3x3/cfop/f2l/f2l

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How to Solve a Rubik’s Cube Benjamin Popp