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How To Solve a Rubik's Cube by Using Algorithms

Never solved a Rubik's cube? Want to? Then follow this rough and ready guide.

How To Solve a Rubik's Cube by Using Algorithms
Interesting Engineering

Love it or hate it, The Rubik's cube is one of the world's most popular puzzles. For many, it is an intimidating challenge, but it doesn't need to be.

With a few simple algorithms and some perseverance, you too can solve one in short order if you haven't before. 

Read on to find out how.  

RELATED: HOW TO CHEAT AND MAKE IT LOOK LIKE YOU CAN SOLVE A RUBIK'S CUBE

 

How long does it take the average person to solve a Rubik's Cube?

If you have trouble solving a Rubik's cube, don't fret, you are not alone. In fact, according to some estimates, only 6% of the population have ever achieved it. Either through a combination of learning algorithms (more on that later), or sheer determination, solving a Rubik's cube is not that taxing if you are willing to work at it. 

In fact, it took the inventor of the Rubik's cube, Erno Rubik, one month to learn how to solve his very own creation.

rubik's cube unsolved cube
Intimidating for many, but exciting for others, the Rubik's cube is a great way to work your grey matter. Source: Rolf Venema/Flickr

The best way to learn how to solve one, without spending hours and days trying to work it out for yourself, is to follow some guides or tutorials. Rest assured this is not cheating. 

Consider this, a standard 3 by 3 by 3 Rubik's cube has nearly 42 quintillion possible combinations, but only a single correct solution. It would take you a very, very long time to attempt to solve it through brute force alone. 

You need to know some strategies, technically called algorithms, to short cut the process. In fact, this is the very reason that algorithms exist in the first place.

Some of those who have gone through the grinder and learned these algorithms, or set moves, can solve a Rubik's cube in double-quick time. It takes, on average, about 45 minutes, or so, to learn these moves. 

Once they become muscle memory, you can trim the process of solving a cube significantly. In many cases, according to some sources, it should be possible for the average person to complete a Rubik's cube in around 20 to 25 minutes

rubik's cube speed solving
The current world record holder for solving the Rubik's cube is Yusheng Du who solved a standard cube in 3.47 seconds. Source: Ruwix

Of course, there are those exceptional people who can solve a cube in less than a minute. The world record for the standard 3 by 3 by 3 cube is 3.47 seconds. Yusheng Du, from China, managed this amazing feat in 2018. 

But try not to compare yourself to this amazing record. Du had been practicing the process for many, many years. 

Is solving a Rubik's cube using algorithms?

In short, yes.

The methods you will use, on the grand and micro-scale, will be by following some set procedures, aka algorithms, to complete the cube. This is essentially what algorithms exist to do. 

So, are you ready to join the 6% who have solved the Rubik's cube? Brace yourself and enjoy the process...

1. First things first, learn your cube

The first thing to do is to become accustomed to your cube. For this guide, we will be focusing on the standard 3 by 3 by 3 cube.

Remember, however, that the following procedures will generally also be applicable to other kinds of Rubik's cube too. 

A standard cube consists of six faces (obviously), with each face consisting of one of six different colors. The middle pieces of each face are fixed, and all other axes (x, y, and z) can rotate both clockwise and counterclockwise.

know your rubik's cube
Modifed from Rolf Venema/Flickr

Guides will usually refer to blocks as consisting of edge pieces (the middle block on the moving edges -- there are twelve of these), corner pieces (the eight corners of the cube), and center-pieces (which are the six fixed bits). 

The colored sides, on a standard cube, are always paired in the following ways: 

  • White is always opposite yellow
  • Orange is always opposite red
  • Green is always opposite blue

This is important to understand and is essential for solving the cube. You will be aiming to move pieces into their correct final position based on these color pairings.

In the following guide and others, we will be referring to certain moves when revealing algorithms for solving the cube. These are standard nomenclature, and they are as follows (courtesy of The Official Rubik's Cube Site): 

rubik's cube solution moves
Letters donate: front face (F), right column (R), left column (L), upper row (U), down or bottom row (D), etc. These terms are relative to the side of the cube facing you. Always keep the cube in this position when performing algorithms, and never rotate the cube unless instructed. Source: Rubik's Cube

Note the use of the letter "i" on some moves. This just means that a move is 'inverted', or reversed.

You will also see greyed-out squares on most images. This just means the block is not in its correct place and its color on the real cube does not matter. 

All moves are a 1/4 rotation. 

For all algorithms provided, it is important to try and visualize the block moving around, and why the move is being made. In most cases, the algorithm will be an even number of moves, to first move the piece and then "repair" the locations of any solved pieces in the rest of the cube (with the exception of the first stage and especially the last stage).

Ok, got that? Let's solve the Rubik's cube, shall we?

2. See the bigger picture

At all times, bear in mind the bigger picture. Solving a Rubik's cube essentially follows a master plan.

  • Stage 1 - Solve the first cross. It doesn't really matter which colored side this is, but the convention is usually the white side first. This means the final layer will be the yellow side. 
  • Stage 2 - Next, you should solve the corners of whichever side you have chosen to start with. By doing this, you will also get the colored "T's" too when the solved layer (aka the first row) is rotated to match the fixed centerpieces on each "side".  
  • Stage 3 - Once stage 2 is complete, flip the entire cube over so that the solved layer (by convention white) is at the bottom and start working on solving the middle layer (aka second row) corners. Remember that the middle pieces are always fixed.
  • Stage 4 - Once complete, you now need to complete the top cross (aka on the third row).  You may also get lucky and have the cube already solved, but this is pretty rare.   
  • Stage 5 - If needed, move the edge pieces of the "Yellow Cross" to their correct places.
  • Stage 6 - If needed, move the corner pieces on the top layer into their correct places. 
  • Stage 7 - If needed, the final step is to get the final layer's (third row's) corners oriented correctly. 

While the above sounds simple in theory, the process requires you to know a few "tricks," in order to achieve it. These are essentially little sub-algorithms used to manipulate the pieces into place. 

We'll dedicate the rest of this article to showing you these algorithms, in order to complete the above "master plan" algorithm. 

3. Solving stage 1 - "The White Cross"

rubik's cube white cross
The "white cross". Remember grey squares are not important here. Note the matching edge pieces to center-pieces. Source: Rubik's Cube

Before we being, time for a confession.

Most of this guide will borrow heavily from the Rubik's cube official guide, as well as the amazing guide from Ruwix.com. The author also only recently learned how to solve a Rubik's cube; and if I can do it so can you!

On with the guide, and good luck.

As previously mentioned, the first thing to do is pick one side to solve first. The convention is to use the white side on a standard cube, but it doesn't really matter

how to solve rubiks cube
We'll go through a real-life solution along with the guide. Here is the starting state of ours. Luckily one of the edge pieces (the red-white piece) is already in place and just needs to be turned to the left 90 degrees. Source: Interesting engineering

However, if one side has some added detail, like a decal or images of some kind, you might want to solve this one first as it will add unnecessary complications later on. 

The aim here is to produce a cross, usually called the "white cross". Since this is the simplest stage, it is highly recommended you attempt to do this through trial and error.

Once you've mastered this, you will be using many of the same moves to solve the middle layer too.

First, move the white side to the top of the cube. For most of the process, the "top" layer will be your "working" layer where you move pieces around and then "drop" them into the lower layers, with the exception of this stage and the final stage (as they are the "top"). 

Move each edge piece to the top row and then move them to match the white on top and the color on a particular side. You need to learn how to do this intuitively, as the starting "state" of a cube will vary widely. 

If you need some help with those pieces that are in the top row but not orientated properly, you can flip them using the following sequence: - 

solve rubiks cube white cross 1
To rotate an edge piece (left image), following the middle sequence. Note: Ri (right column down), U (top layer to the left), Fi (front face counterclockwise), Ui (top layer to the left). Your goal is to make the cross on the right. Source: Rubik's Cube

Rinse and repeat for all other edge pieces. Once your cube looks like the image on the right above, move to the next stage. 

Below is a worked example of the steps for moving one edge piece into place. The exact location and method needed for yours will vary, obviously.

Remember, we have greyed out any blocks where the exact color is not important on your cube. 

solve rubiks cube edges
In this example, we can solve two pieces in one algorithm (on the left is the starting condition, on the right the result). Note the cube has been turned 90 degrees to the left in the righthand image. Make sure the red centerpiece is facing you when performing moves (indicated by the red arrow).

1. Rotate the upper level to the left (U) to move the red edge piece above the red centerpiece. 2. Rotate the upper level again (U), and then move the front face counterclockwise (Fi). You will need to also move the top row to the right (Ui) to align both red and blue edges with their correct centerpieces.

Source: Interesting engineering

Keep moving the edge pieces into their correct places until you have the "White Cross". You can refer to the other guides if you need help with some of the pieces, but we stress that you should try to solve this on your own. 

When you have the white cross, move to the next stage, but only if the edge pieces are in the correct order (i.e. match the fixed centerpieces on each side). 

rubiks cube white cross
The "White Cross". Source: Interesting Engineering

4. Solving stage 2 - Solving the top corners

Next up is to finish off the white side with the corner pieces in the right places. While it might sound tricky, it really just requires a little thought and practice.

Below is an example of getting one into place from our real example.

rubiks cube corners
An example of solving a corner piece. Orange is the front face in this example. You are effectively moving the white-orange-green corner piece into place, fixing it in place at the back of the cube, restoring the position of the front face, and bringing the new complete white-orange-green-red row into place. Notice the complete white face and "T" shapes on the sides. Source: Interesting engineering

If you are struggling with other scenarios, check out any of the full tutorials we have provided above to help you out. But, again, we recommend plugging away yourself to solve this stage. 

Once complete, turn the cube over so the white face is on the bottom. You will not be touching it for the next stage. 

5. Solving stage 3 - Solving the middle layer

This stage is relatively simple, and you only really need to know a couple of set moves, or algorithms. In most cases, you will be shuffling the middle-layer edges from the top layer to left or right on the middle layer. 

In all cases below, make sure you have orientated the piece to be moved above its matching center-piece on the side of the cube. E.g. if the color facing you is red, make sure you move the top row until the correct edge piece is above the red center-piece facing you. 

Remember, whenever completing these algorithms, always keep the front face in front of you and never move the cube as a whole.

Here is how you move one piece to the right. We'll dub this the "move-to-the-right" algorithm. 

rubiks cube middle to right
Algorithm to move the red-blue middle piece on the top row to its rightful place in the middle/second row. Here the front face is the blue side. Note the first four moves put the piece into place and the last four restore the base. Source: Interesting Engineering

If you need to move it to the left, here is how you do that. We'll call it the "move-to-the-left" algorithm. 

solve rubiks cube top middle to right
Algorithm to move the orange-blue middle piece on the top row to its place on the left-hand side in the middle/second row. Here the front face is the blue side. Note the first four moves put the piece into place and the last four restore the base. Source: Interesting Engineering

Sometimes you may need to move a misaligned middle or second layer edge piece to the top and then back down again. Here is how you do that move.

rubiks cube mid to top
Notice that this is the same move as the moving-to-the-right algorithm above. Once in place on the top row, simply rotate the top row to the right (to match green to green). Now make the green face your front face, and complete the "move-to-the-left" algorithm above to put the same piece into the second row. Source: Interesting Engineering.

With the middle, or second, row complete, it is time for the most complicated part -- the top layer. Well done, you are 66% of the way there.

6. Solving stage 4 - Making the "Yellow Cross"

Now for the top row. First, we need to create a cross again, as we did at the beginning. This will be slightly more complex than the "White Cross", as you can imagine. 

For this stage, don't obsess over getting yellow edge pieces in the correct order. Our goal is to simply get the yellow side of each edge piece facing upwards. 

If you are lucky enough to already have a full cross, you can skip this stage. If not, you will need to perform a single algorithm multiple times, until you reach the end goal. 

And here it is, courtesy of the makers of this awesome puzzle...

solve the rubik's cube yellow cross
Source: Rubik's Cube

When you reach any of the stages above, ensure you turn the upper layer to match its orientation. Again, don't fret about the side colors just yet. 

With the "Yellow Cross" complete, it is time to get those top edge pieces in their right places...

7. Solving stage 5 - If needed, move the "Yellow Cross" edge pieces into the right order

If, by chance, the edge pieces from stage 4 are already in the correct order, skip to stage 6 below.

If not, you will need to perform some more sets of moves to get them into their proper places. You can swap them around by performing the following algorithm.

In all cases, make sure you orientate the top row so that at least one of the pieces will end up on the correct side of the cube. Rotate the upper row to get the edge pieces you need to be aligned with the sides they need to move to. 

shuffle edge pieces top row
If you need to move the edge pieces around on the upper/top row, perform this algorithm. In this example, the red side is your front face. You may need to do this a few times to get all edge pieces in their correct places.  Source: Interesting Engineering

 With the edge pieces now aligned properly, it is time to deal with those pesky top corners. 

8. Solving stage 6 - Orientating the top corners properly

With only four pieces left to move, you might think the worst of it is behind you? Don't get cocky, this is the stage that usually foxes most novices. 

The first thing to do is to get them into the right spot. Don't concern yourself with their orientation, just yet. 

Find a piece that already happens to be in the right place (its three sides match the surrounding colors on the cube's edge). You may need to move the upper row to find one. 

Orientate the cube so that this corner piece is in the top right of your front face. Then perform the following algorithm to cycle the corner pieces around. 

rubiks cube get corners in place
Algorithm to cycle corner pieces around. You will likely need to do this a few times until all corners are in place. Don't worry about getting the yellow sides up, just yet. Source: Interesting Engineering

You will likely need to do this a few times, keeping the same reference corner piece in the top right -- it will return to the same position when the algorithm is complete. 

If none exists, perform the same algorithm until one appears and then rinse and repeat.

9. Solving stage 7 - Finish the cube!

With all the corner pieces in their right positions, the final and the most fun stage is to orient them correctly -- aka get those yellow sides facing upwards. The algorithm is very simple for this part, but it often freaks out newer Rubik's cube users. 

At the end of each algorithm sequence, your cube will look completely messed up. Don't worry, trust the process and your cube will be solved in very short order. 

Hold the cube in your hand and choose one of the corners to start the process. Make sure it is in the correct position (aka the surrounding cube face colors are the same as those, in any order, on the corner piece). 

Now perform the following algorithm until the piece is orientated correctly. You will usually need to do this two or four times. 

solve rubik's cube finale
Algorithm to correctly orientate a top row corner piece. You will need to repeat this between two and four times until correctly orientated. Source: Interesting Engineering

If you need to do the same for any other corners, keep the same side facing you as before (this is critically important); rotate the upper row to move the piece into the top right, and repeat the procedure two to four times. Rinse and repeat for all other corners. 

We have to stress once again: trust the process. The rest of your cube will appear to be completely messed up but it will all come together in the end. 

With the top row solved, simply move to the left or right to complete the cube.

Congratulations, you did it!

Now that you know how to solve the standard 3 by 3 by 3 Rubik's cube, you can practice until you get the processing speed down to impressive levels. Who knows, you may become the next Guinness World Record holder? 

One has to dream...

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