How to solve a 2x2 Rubik's Cube

Introduction

The 2x2x2 Rubik's cube, or in its official name- the Pocket Cube, is another puzzle in the Rubik's cube series, invented by Erno Rubik. It is considered the "easy" version of the Rubik's cube. You will find out that solving the 2x2 cube is much easier than solving the classic 3x3x3 cube. 

If you already know how to solve the 3x3 Rubik's cube..

If you can already solve the classic Rubik's cube, then lucky you- you already know how to solve a 2x2 cube! Here is a nice perspective of the puzzle: the 2x2 cube is actually a regular 3x3 cube, without the edges and the center pieces. So basically solving the 2x2 cube will be identical to solving only the corners of the 3x3. You will be surprised that some of the algorithms you'll have to know are identical to those you'll need in order to solve the 2x2 cube, and you already know all of them if you are familiar with the speedsolving method.. 

Before starting the solution guide, make sure you know the Rubik's cube move notations. For 2x2, the notations are exactly the same (same faces, same letters, same cube rotations, just without the "middle layer moves" – as there aren't such in the 2x2 cube)

The 2x2 Rubik's Cube solution

Step 1: Solving the first layer

This step is identical to step 2 of the 3x3 cube solution. Choose a color to start with (Most popular color to start with is white or yellow – In this guide I chose yellow). Choose a corner that has this color (yellow in our case), and bring the other 3 corner pieces to it. Make sure that you solve the corner pieces correctly in relation to each other (also the side colors of the corner pieces should fit each other, not only the yellow. See image- right/wrong). 

There are 3 different cases to solve a corner piece to its correct position without harming the other corners: 

F D F'

R' D' R

R' D2 R D R' D' R

Step 2: Orienting the last layer pieces

Flip the cube upside down (the solved layer should be on the bottom now). In this step the goal is to orient the last layer pieces. The result should be that the opposite color to the color we started with will be completed (In our case: the opposite color to yellow is white). Note that unlike the first step, here the permutation of the corners does not matter, meaning that they don't have to be correctly solved in relation to each other (side stickers don't have to fit). 

There are 7 possible cases of last layer orientations (not including the already oriented case): 
(The gray color means the sticker is not the upper face color. The bars to the sides show where the upper face color is. In our case it's white, not yellow. It doesn't matter of course.) 

Case #1

R' U' R U' R' U2 R

Case #2

L U L' U L U2 L'

Case #3

R2 U2 R U2 R2

Case #4

F [R U R' U'] [R U R' U'] F'

Case #5

F [R U R' U'] F'

Case #6

[R U R' U'] [R' F R F']

Case #7

[F R U' R' U' R U R' F']

It is best to learn all the 7 algorithms. However, it is possible to completely solve this step using only 1 algorithm – the first algorithm. The idea is to execute this algorithm from different angles until its suitable case shows up, then execute it one more time and solve the step. It is possible to solve all possible cases within 3 executions, or 2 if you use also its mirror algorithm (case #2). 

The first algorithm orients 3 corners counter-clockwise and leaves the 4th corner intact (its mirror algorithm, case #2, does the same, but clockwise). Before executing, try to think from which angle executing this algorithm will leave only 1 oriented corner (can be done within 1 execution from all cases), than just apply the suitable algorithm (case #1 or #2). You can execute algorithm #1 twice instead of the using #2 algorithm when it's needed (in a case a clockwise rotation needed (case#2). Doing counter-clockwise twice for the corners will be just like doing a clockwise orientation, which will solve them.) 

Note that 6 of these 7 algorithms are exactly the same algorithms being used in the speedsolving method of the Rubik's cube. You can see it is the same 7 possible cases when all the edges of the 3x3 are oriented: OLL algorithms page. However, since there are no edges to preserve, we can use shorter algorithms from other cases of the traditional OLL of the 3x3 Rubik's cube, as long as they rotate the corners as we need: 

• For the first case best algorithm is the anti-Sune (OLL algorithm #26)
• For the second case best algorithm is the Sune (OLL algorithm #27)
• The third case is special: a shorter algorithm can be applied, which does exist in the 3x3 OLL, however OLL algorithm #21 is very nice)
• For the fourth case best algorithm is the easiest L (OLL algorithm #48)
• For the fifth case best algorithm is the first T (OLL algorithm #45)
• For the sixth case best algorithm is the second T (OLL algorithm #33)
• For the seventh case best algorithm is the first Fish (OLL algorithm #37)

Step 3 (and last): Permuting the last layer pieces

In this step the goal is to permute the last layer pieces so they will be also correctly solved in relation to each other, and not only correctly oriented. This step is very similar to step 5 of the 3x3 solution (beginner's method) (-also the same algorithm can be applied, it is just that the one I show here permutes the corners clockwise and not counter-clockwise). The way to solve this method is by looking for 2 corners that are correctly permuted in relation to each other (can be easily recognized by the fact that 2 correctly solved corners in relation to each other has the same color on their mutual face. Look for the same color in 2 adjacent corners). If you don't have 2 corners that are correctly permuted, just execute the following algorithm below from any angle that you want. After that execution, 2 correctly permuted corners will show up. 

Then: 

• Do some U turns so the 2 adjacent same colors will line up with their color on the bottom layer. Rotate the cube so that this solved color will be on the right face- see image above.
• Do U' once.
  The effect of this move is that the front-left corner will become "solved" now, and the 3 other corners will require a clockwise rotation between them. This is exactly what the next algorithm does.
• Execute the following algorithm: (This is the Aa-perm algorithm. l' replaced for L' because no middle layer)

L' U R' D2 R U' R' D2 R2

That’s it! You have just solved the 2 by 2 Rubik's cube! Congratulations! Keep practicing on solving the first layer and learn the algorithms by heart, so you could solve the 2x2 cube without needing them written around you (They are also useful for 3x3 speedcubing!). If you didn't solve the 3x3 Rubik's cube yet, it's just about the time to start, you already have much of the basics! Congratulations!

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