How To Solve A 3x3x3 Rubiks Cube - Standard Cube - 3x3 Rubik's Cube

Continuing with this series of tutorials, we will see now How To Solve A 3x3x3 Rubiks Cube.

To learn how to solve a 3x3 Rubiks Cube it's not more difficult than to learn how to solve a 2x2 Rubiks Cube.

In this tutorial you will find all the necessary information to solve the Standard Cube.

However it's advisable to read how to solve the Junior Cube first, since the techniques applied to the resolution of the Junior Cube will be of great help to solve the Standard Cube.

All the learned movements for the resolution of the Junior Cube will be used in the resolution of the Standard Cube and a few more will be added, achieving in this way a gradual learning curve.

How to solve a 3x3x3 Rubiks Cube
How to solve a 3x3x3 Rubiks Cube

If you have followed the steps of How To Solve A 2x2x2 Rubiks Cube, the practice will be useful.

How to solve a 3x3x3 Rubiks Cube

In order to understand How To Solve A 3x3x3 Rubiks Cube, you need to be familiar with the notation. If you don't know it, please read 'How to solve a Rubiks Cube' before continuing.

First a description of the algorithm will be shown, and then the movements.

For the purposes of the following tutorial, a series of colors will be chosen for the faces, you can choose others.

Keep in mind that the color of the Centre Piece determines the colour of the Face.

Pieces and Layers

  • Corner .. - a physical corner piece. Has three sides. There are eight corners.
  • Edge .... - a physical edge piece. Has two sides. There are twelve edges.
  • Face ..... - one of the sides of the cube.
  • Layer .... - the cube consists of three layers (Top/Middle/Bottom).
 
 

How To Solve A 3x3x3 Rubiks Cube - Description Of The Algorithm

The algorithm is divided in seven steps. In each step a series of moves are executed to solve a cubie. The series repeats (non resolved cubies) until completing the step.

(For a better understanding of the description, the black stickers represents an irrelevant color for that move.)

Step 1, Bottom Layer Edges

The first stept is to make a Cross on the Bottom layer.

Making sure the second color on each edge piece matches the color of the center cubie on each side face.

Step 2, Bottom Layer Corners

Place the corner pieces in position on the Bottom layer.

When all the corners are in position, the Bottom layer is solved.

Step 3, Middle Layer Edges

Place the edge pieces in position on the Middle layer.

When all the edges are in position, the Middle layer is solved.

At this point, the Bottom Layer and the Middle Layer are complete, this is known as F2L (First 2 Layers)

Step 4, Last Layer Edges

The first step towards solving the Last Layer, is to make a Cross on the Top Face, without caring about the other colors around the side.

Step 5, Permute The Top Layer Edges

If the edge pieces are not in their solved positions, the next step is to position the edge pieces correctly.

Step 6, Orient The Top Layer Corners

Place the corner pieces in position on the Top layer, without caring about the other colors around the side.

Step 7, Permute The Top Layer Corners

If the corners are not in their solved positions, the next step is to position the corners correctly.

Congratulations! You have solved the cube.

How To Solve A 3x3x3 Rubiks Cube - Algorithm

Now that you understood the method, it is time to put in practice.

Step 1, Bottom Layer Edges

Choose a color for the Down Face and a color for the Front Face: (let's take Yellow and Red)

Find in the Top Layer the Edge Piece of both colors.

There are two possible states: The Down color (Yellow) is on the Upper Face, The Down color (Yellow) is around the edges (turn the Top Layer if necessary).

Use one of the following procedures to solve the cubie:

Down Face color on the Upper Face

U - F2
U - F2

Down Face color around the edges

R' - F - R
R' - F - R

The move [R] restores an Edge Piece that may have been removed of its place.

If the Edge Piece is in the Middle Layer or in the Bottom Layer but not solved, move it up to the Top Layer.

Edge Piece in the Middle Layer

R - U - R' - F2
R - U - R' - F2

The move [R'] restores an Edge Piece that may have been removed of its place.

Edge Piece in the Bottom Layer

R2 - U - F2
R2 - U - F2

Choose another color for the Front Face and repeat the procedure until completing the cross on the Bottom Face.

Step 2, Bottom Layer Corners

Find in the Top Layer a Corner Piece with the color of the Down Face (Yellow).

Look at the other two colors of the piece (Red and Blue, for example), place the Corner Piece (turn the Top Layer) in-between the two Center Pieces of the same colors.

There are three possible states:

Down Face color on Front Face

F' - U' - F
F' - U' - F

Down Face color on Right Face

R - U - R'
R - U - R'

Down Face color on Upper Face

R - U2 - R' - U' - R - U - R'
R - U2 - R' - U' - R - U - R'

If the Corner Piece is in the Bottom Layer, move it up to the Top Layer and use the above procedure.

Corner Piece in the Bottom Layer

R - U - R' - U'
R - U - R' - U'

Step 3, Middle Layer Edges

Find in the Top Layer an Edge Piece which do not have the color of the Upper Face (White), if not see below edges trapped.

Choose a color for the Front Face (Red), turn the Top Layer to match the color of the Edge Piece with the same color of the Centre Piece.

There are two possible states:

Edge Piece to the Right Face

U - R - U' - R' - F - R' - F' - R
U - R - U' - R' - F - R' - F' - R

Edge Piece to the Left Face

U' - L' - U - L - F' - L - F - L'
U' - L' - U - L - F' - L - F - L'

In case of edges trapped, execute one of the procedures above to replace the trapped edge with an edge from the Top Layer.

If for example, the Green-Red Edge Piece is trapped in the Middle Layer as is shown, execute the first procedure in order to replace it with the Gray Edge Piece. Once the Green-Red Edge Piece is on the Top Layer, then continue as normal.

(The gray piece represents any two-colors Edge Piece)

Edge Trapped
Edge Trapped

Step 4, Last Layer Edges

There are three possible states: the Dot, the Line, the L.

The Line

F - R - U - R' - U' - F'
F - R - U - R' - U' - F'

The L

F - U - R - U' - R' - F'
F - U - R - U' - R' - F'

The Dot

F - R - U - R' - U' - F' - U2 - F - U - R - U' - R' - F'
F - R - U - R' - U' - F' - U2 - F - U - R - U' - R' - F'

Identify the state and apply some of the above procedures until the cross is formed.

Step 5, Permute the Top Layer Edges

If turning the Top Layer the color of the Edge Pieces match the color of the Centre Pieces, go to the following step, is this is not the case, try to align the Top Layer so that only one Edge Piece is solved (if not, see below).

There are two possible states:

Permute Three Edges Counter-Clockwise

R - U - R' - U - R - U2 - R'
R - U - R' - U - R - U2 - R'

Permute Three Edges Clockwise

R - U2 - R' - U' - R - U' - R'
R - U2 - R' - U' - R - U' - R'

If it not be possible to position the Top Layer so that only one edge is solved, execute one of the procedures above to get one Edge Piece on Top and then proceed the same as before.

Step 6, Orient the Top Layer Corners

A Corner Piece which needs to be oriented is one which does not have the Upper Face color (White).

Identify the corners that need to be oriented, it is possible to have to twist 2, 3, or 4 Corner Pieces.

Turn the Top Layer so that the Corner Piece which needs to be oriented is at the Back-Right.

There are two possible states: Upper Face color (White) on the Right Face or Upper Face color (White) on the Back Face.

Upper Face color on the Right Face

R - D - R' - D' - R - D - R' - D'
R - D - R' - D' - R - D - R' - D'

Upper Face color on the Back Face

D - R - D' - R' - D - R - D' - R'
D - R - D' - R' - D - R - D' - R'

After orienting the first Corner Piece the First Two Layers are scrambled.

DON'T ROTATE THE CUBE, MAINTAIN THE FRONT FACE.

Turn the Top Layer so that the next Corner Piece which needs to be oriented is at the Back-Right and then proceed the same as before.

Once you have twisted all the corners the First Two Layers will have restored itself.

NOTE: For this procedure to work correctly, you need two, three or four corners which needs to be oriented.

If you have only one corner not well oriented, performing the following movements the four corner pieces will need to be oriented.

(Place the wrong Corner Piece at the Front-Right)

U - R - U' - L' - U - R' - U' - L
U - R - U' - L' - U - R' - U' - L

Now, continue with the Step 6 as normal.

Step 7, Permute the Top Layer Corners

Turn the Top Layer so that a Corner Piece is located in its solved position (if not, see below).

Turn the cube in your hands so that you hold it with the solved corner at the Front-Left position.

There are two possible states:

Permute Three Corners Counter-Clockwise

R2 - B2' - R - F - R' - B2' - R - F' - R
R2 - B2' - R - F - R' - B2' - R - F' - R

Permute Three Corners Clockwise

R' - F - R' - B2' - R - F' - R' - B2' - R2
R' - F - R' - B2' - R - F' - R' - B2' - R2

If it not be possible to locate a Corner Piece in its solved position, execute one of the above procedures to get one.

Now you know How To Solve A 3x3x3 Rubiks Cube.

How to Scramble a Rubik's Cube

A good friend from Finland, Akseli Palen, has brought an interesting subject, How to scramble the Cube?

Certainly, one can use methods such as spinning the faces of the cube in any direction for some time, or give it to someone else to spin it around for us.

Although it may seem to us that the cube is scrambled, most of the time when we scrambled a solved cube this remains "partially assembled" because we do always redundant sequences.

Is there a right way to scramble a Cube?

Yes. In competitions algorithms are used (scrambles) to ensure fairness between competitors.

The procedure is as follows:

  1. A random number of movements are generated (25 to 30)
  2. For each movement a random face is chosen (U,D,L,R,F,B) and a move (X, X' X2)
  3. Exceptions:
  • a) The following movement must not be of the same face as the previous
  • b) If two faces have moved in the same plane consecutively, these faces are discarded for the next move (ie: move n -> U; move n+1 -> D; move n+2 -> choose between: L,R,F,B)

Algorithm

Akseli has developed a web application to properly scramble the Rubik's Cube, which I recommend that you visit, bookmark and tell your Rubik's Cube fan friends.

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        Acknowledgement : Table Of Contents by Darkside
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Comments 59 comments

Nathan 7 years ago

It might just be me messing up but in some pictures I think you have the arrow pointing the wrong direction!You down and down reverse arrows are backwards! ...I think...


StefanMDP profile image

StefanMDP 7 years ago Author

Hi Nathan!

The images are made seeing always the Front Face. When you make a turn, try to imagine a clock on the face.

For the Down Face the clock points down. You will see this way that the arrows are correct.

Still confused? Tell me.


Nathan 7 years ago

Oh I see now, I imanged the clock was always on the front face. Thanks.


thx bro 7 years ago

thx bro


i love britney spears and m.j. 7 years ago

this is sooooo freakin amazing and soo cool!!!!!!!!!!!!!!!!!!!!!1


notorious_HAI 7 years ago

I wasn't sure what to do this weekend because it's cold and raining in Adelaide. Now I have something to do....


horuixiang 7 years ago

is nice to play


Joel 7 years ago

I feel a little mixed up because the algorithm is inverted from the one I learned as a kid in grade school. I used to do this puzzle in no time.


StefanMDP profile image

StefanMDP 7 years ago Author

Hi Joel

Thanks for stopping by.

There are several algorithms to solve the cube. Here I am presenting one of the simplest for beginners, certainly it is not the quickest.

But You know, the important thing is the satisfaction of being able to solve it, isn't it?


jonty 7 years ago

Very well written hub .....

very much informative ......

Thank you very much for your great hub, for good advice, good wishes and support. Thanks for sharing your experience with all of us.


Mike 7 years ago

Do you have an algorithm guide for solving the bottom corners with the middle edges at the same time?


StefanMDP profile image

StefanMDP 7 years ago Author

Hi Mike, Thanks for stopping by.

No, sorry, only this tutorial for beginners.


Sexy jonty profile image

Sexy jonty 7 years ago from India

nice solve trick .....


C. N. 7 years ago

There is something strange on step 7, "Permute the top layer corners":

Shouldn't that B2 be B2'? The arrow (and the movement) are counterclock wise.


StefanMDP profile image

StefanMDP 7 years ago Author

Hi C.N.

You are right, according to the arrow it should be B2'.

Anyway, the result of the steps is correct since B2 and B2' is the same movement.

Thanks for noting it, I will correct the images.


justsandandsand 6 years ago

I asked permission

I created this website link on my blog

I salute with explanations and pictures on your website

clearly explained

Sandhi, an Indonesian


S.M.S 6 years ago

Hey man, I have a problem. I solved the whole cube besides two corners. They need to be rotated but i cant do it. There in the correct position, just not allinged.


StefanMDP profile image

StefanMDP 6 years ago Author

Hi.

Did you perform Step 6?

(orient the top layer corners)


Dadio 6 years ago

Hi, I used your beautifully done graphics and clear and concise directions once again (I did the 2x2x2 earlier today with your tutorial) to solve the 3x3x3 that I got as a gift in 1983 and had never gotten past the first two layers solved. I never tried using any instruction whatsoever until today and I tried several other sites with no success until I came across yours. Thank you very much,again...you are too cool! I wish you were in charge of making diagrams for the shop manuals I use to repair my motorcycle, cars, and mountain bikes! ps. you are like Charlie from the tv show "numbers" explaining a complex theory to less enlightened minds so they can grasp and utilize the concept to achieve a goal, that is a gift... thanks for sharing it with "us".


StefanMDP profile image

StefanMDP 6 years ago Author

Thanks Dadio, a big hug.


comady25 6 years ago

Very good. Step 3 is a little confusing though...:/


StefanMDP profile image

StefanMDP 6 years ago Author

Hi Comady

I suppose that you refer to the Trapped Edges. I have added an image so that it is clearer.


person 6 years ago

help meeeeeeeeeeeeeee!!!!!!!!!!!!!!! I dont understand this


StefanMDP profile image

StefanMDP 6 years ago Author

Send me your cube, I will solve it for you. :)


Arpit Mathur 6 years ago

I am not able to make it


StefanMDP profile image

StefanMDP 6 years ago Author

Follow the instructions, and you will be able to make it. :)


How To Solve A Rubix Cube 6 years ago

long instrucation but if you will follow them step by step you will do it in the end :)


Jello solves cubes 6 years ago

Does it matter if i use a dirrerent brand of a cube instead of a rubix cube? The positions of the colors are dirrerent too


StefanMDP profile image

StefanMDP 6 years ago Author

If it's a 3x3x3 cube, the brand does not matter.

Here is taken as an example a cube with standard color scheme: Yellow opposite White, Blue opposite Green, Red opposite Orange.

In the 3x3x3 cube, the center pieces are fixed, making it easier to determine the color scheme. If it is not equal to that used here, once you could determine the scheme of your cube, take any face as front and replace the colors shown here by the colors of your cube, face to face.

Good luck!!


arive_angelo@yahoo.com 6 years ago

this tutorial for new beginners is so dificult because they can"t understand it very well;


StefanMDP profile image

StefanMDP 6 years ago Author

Have you been speaking with 35000+ people who have read this tutorial?

Or do you speak for yourself?


Smeone765 6 years ago

Good tutorial!!!!

Very nice indeed!!


Rubik's begginer 5 years ago

Wow, thank you so much. I have been to about 1 million different websites and they were all so hard to follow and confusing, but this is so useful! Thanks again! I voted up, useful and awsome ;)


StefanMDP profile image

StefanMDP 5 years ago Author

Hi, thanks for stopping by.

I am glad to have been of help.


How to Solve a Rubix Cube 5 years ago

Interesting tutorial. Thanks!


yusuf_parity 5 years ago

I can solve my cube in 39 sec.


StefanMDP profile image

StefanMDP 5 years ago Author

Good for you! :)


Arayende 5 years ago

Hey! Fantastic website, this was a wonderful help! i've been putting off writing a paper for the afternoon and this certainly gave me something to do! (Grinning my head off at the cube that hasn't been solved for the entirity of its life, so exciting!) Thank you so much for putting this up, it was cleary explained and easy to understand for us lesser minds and the pictures were a great help. You made my week with this! Thanks again!


StefanMDP profile image

StefanMDP 5 years ago Author

Hi Arayende.

Thanks for stopping by. I'm glad you found this useful.


fraggler profile image

fraggler 5 years ago from Brisbane, Australia

The good old rubiks cube is great for taking on long plane trips...but even with the instructions it can become frustrating. Awesome fun though and I think more should use them - especially kids!


BENNY 5 years ago

thank you so much.

You've spent a lot of valuable time for this! Thanks again!


StefanMDP profile image

StefanMDP 5 years ago Author

Hi Benny.

Thanks for your comment.

If this tutorial has been helpful for you and others, it has been time well spent.


Mens Gift Ideas 5 years ago

Wow, I have had a cube at home for over 20 years and have not been able to finish it.

I'm going to give it a try following your instructions.

thanks


Viola 5 years ago

thanks


Seba 4 years ago

I have been looking for this "algorythm" for a while. This is the best one!! Thank you very much for your great explanation! Great Job


xeli profile image

xeli 3 years ago from Tampere, Finland

Thanks a lot for this tuto. I have read it through so many times lately :)

For anyone learning the cube, and especially if you are counting seconds, there is a need to shuffle the cube randomly. I wanted to be sure about that so inspired by this article I created an web application for that. Check it out :)

http://shuffle.akselipalen.com


StefanMDP profile image

StefanMDP 3 years ago Author

Hi Akseli

When I wrote this tutorial I did it in the hope that it might be useful to those who wish to solve their Rubik's Cube for the first time in a simple way.

Always made me happy to know that this modest tutorial has been helpful to someone.

Through questions and comments, this tutorial has been improved, becoming more clear.

Of course the feedback from the readers is something that one wants and expect when writing an article online.

But I must say, never in my mind I thought that this tutorial could be a source of inspiration.

Man, you've done a great tool and is a very good complement for this tutorial, I will add it.

Thank you very much Akseli


sdelandtsheer profile image

sdelandtsheer 3 years ago from Ferrara, Italy

I was thinking about writing such a hub. Hopefully I checked before and found your version, which is better illustrated than anything I could have done myself. I keep the page for future reference, because you make the last few steps with different formulas as me. Awesome post. Thank you!


StefanMDP profile image

StefanMDP 3 years ago Author

Hi Sébastien

Thank you for your kind words.


Florin 3 years ago

Hi, i have a problem on step 6. I have 2 corner pieces and after orienting the first corner piece, i rotate the top layer so the last corner piece is in the back right position and if i orienting again the last corner piece the yellow face is not restored. I tried to don't rotate the top layer after i oriented the first corner piece and to rotate the cube but the yellow face is not restored too. What is wrong?


StefanMDP profile image

StefanMDP 3 years ago Author

Hi Florin

The step orient the top layer corners is a tricky step in all the cubes. In this step you should maintain the front face during the whole process.

You should:

A- Select the Front Face.

B- Turn the top layer so that the corner you are working on is at the Back-Right position (ie North-East as you look at it).

C- Identify whether the upper face color (Yellow, following the example) sticker on the corner sits on the Right face or the Back face.

D- Apply the correct move so that the upper face color is moved to the top.

E- STOP. Now the first layer are scrambled. DON'T ROTATE THE CUBE IN YOUR HANDS, MAINTAIN THE FRONT FACE and turn the top layer to bring the next corner that you want to work on into the Back-Right position. Go back to C.

Hope this helps


xeli profile image

xeli 3 years ago from Tampere, Finland

You wrote in a recommendation for the shuffler app, awesome! Thank you, I really appreciate this :) The app has received nice amount of traffic since \o/


NancyBeth profile image

NancyBeth 2 years ago from Torrington, Wyoming

Thanks Stefan, this is the best link to 3x3 algorithms simply because when I show off to my friends on how to solve it looks so technical they just don't understand. love it! I always show the first part without the pictures and that really gets me laughing at them when they say Oh My Gosh, what is all that?! LOL.

p.s. to those of you with the bump cube the first layer is easiest to solve the first tallest layer then from there solve as a 3x3 as shown above.

Hey Stefan, you should do a page on that cube too.


Kylia 20 months ago

Damn, I wish I could think of sotmiheng smart like that!


Idalee 20 months ago

Son of a gun, this is so heufpll!


e.c 17 months ago

thank you for your help. without this I can't understand the logic of rubric's cube


Linda Robinson60 profile image

Linda Robinson60 3 months ago from Cicero, New York

Hello StefanMDP so nice meeting you. And just wanted to say how interesting your hub is about the rubik cube. It is such a simple yet complex challenge and you explained with such detail and outstanding photos. I look forward to following you and reading more of your hubs. Linda


StefanMDP profile image

StefanMDP 3 months ago Author

Hi Linda.

Thanks for stopping by.

When I wrote this Hub a bit more than 7 years ago (time flies, don't you think?) I wrote this with the idea that it was a simple method to understand for beginners. When I hit the "Publish" button, a doubt arose in my mind: Will it really be easy to understand?.

Words like yours have helped me to clear this doubt.

Still seven years later, I feel the same satisfaction and gratitude as the first time someone wrote me a "thank you for the Hub".


Erica Dumale 2 weeks ago

amazinggggg i learn and enjoy

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