How to Solve 2×2 Rubik’s Cube: A Beginners Guide

If you’re looking to learn how to solve a 2×2 cube, you’re in the right place! The 2×2 Rubik’s Cube, also known as the Pocket Cube, is a simpler version of the standard 3×3 cube, making it an ideal starting point for beginners. Although it lacks center and edge pieces, solving it still involves understanding basic algorithms and techniques. In this guide, we’ll walk you through the steps to master the 2×2 cube, starting from solving the first layer to completing the entire puzzle. Let’s get started!

Terminologies in a 2×2 Rubik’s Cube

1. Color Scheme

The 2×2 Rubik’s Cube, often known as the Pocket Cube, is an even-layered puzzle with a fixed colour scheme of white against yellow, red against orange, and blue against green.

b. The color scheme of the Rubik’s Cube is fixed and follows: white is opposite to yellow, blue is opposite to green, and red is opposite to orange.

2. Pieces

In contrast to the standard 3×3 Rubik’s Cube, the 2×2 Rubik’s cube contains 8 corner pieces total—neither centres nor edges.

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Notations of a 2×2 Rubik’s Cube

Before starting to solve the 2×2 Rubik’s cube it is necessary for us to know few notations to further strengthen our understanding of the puzzle:

1. R & R’ Notation

R (Right): Rotate the right layer of the Rubik’s cube clockwise i.e. right side upwards.

R’ (Right Prime): Rotate the right layer of the Rubik’s cube anti-clockwise i.e. right side downwards.

2. L & L’ Notation

L (Left): Rotate the left layer of the Rubik’s cube clockwise i.e. left side downwards.

L’ (Left Prime): Rotate the left layer of the Rubik’s cube anti-clockwise i.e. left side upwards.

Note: The left and right movements are opposite to each other.

3. U & U’ Notation

U (Upper): Rotate the upper layer of the Rubik’s cube clockwise i.e. upper side towards the left.

U’ (Upper Prime): Rotate the upper layer of the Rubik’s cube anti-clockwise i.e. upper side towards the right.

4. D & D’ Notation

B (Down): Rotate the down side layer of the Rubik’s cube clockwise i.e. down side towards the left.

B’ (Down Prime): Rotate the back side layer of the Rubik’s cube anti-clockwise i.e. back side towards the right.

Note: Any alphanumeric representation signified by ”2” after the alphabet, for example, U2 denotes moving that particular layer twice in any direction (since the puzzle has four sides, two movements on each side are equivalent).

How to solve the 2×2 Rubik’s Cube?

Prior to delving into the 2×2 Rubik’s cube, we need to select a colour. For ease of learning, we choose white as the starting color; but, after you get proficient in the 2×2 Rubik’s Cube, you can become colour neutral and begin from any side to solve the puzzle.

Step 1: Solving the 1st Layer (White Side)

The first step is to hold a white corner piece with the white side facing the top. Before we can start solving the remaining white pieces, we need to properly position them before inserting them onto the top layer. To insert the correct edge piece, refer to the colour scheme of the first corner piece, as the 2×2 lacks centres.

 a. White face on bottom left layer:

By executing D L D’ L’, you can insert an edge piece from the left bottom layer to the top layer.

2. White face on bottom right layer:

Perform D’ R’ D R to insert it if it is on the right layer from the right bottom layer.

3. Twisted corners on top layer:

Sometimes the corners on the upper layer are correct but twisted. This is readily solved by placing the twisted corner on the correct layer and performing (R’ D’ R D) (R’ D’ R D) once or twice.

Note: (R’ D’ R D) (R’ D’ R D) is a corner twisting algorithm and if performed thrice it returns the corner to its original state.

4. Special case

a. White facing the bottom side (i.e. opposite to white)

1. In this scenario, we must twist the corner before solving the first layer, as in this type of corner piece we may not be able to face the white color. 
2. First, perform D moves to bring this corner to the right layer, and make sure the top corner of the white layer is unsolved. 
3. Then, perform R’ D2 R; now that corner must be on your left layer.

b. Corners incorrectly positioned in Top Layer

Sometimes we encounter a situation in which a white corner is in the top layer but incorrectly positioned. In this case, we must take the corner from the top layer and move it to the bottom layer.

If the white corner is on the right layer, face it and bring it to the bottom layer with R’ D R. And, if the white corner is on the left layer, face it and bring it to the bottom layer using L D’ L’.

Orient it and solve using the procedures outlined in 1/2/3. Thus, the first layer is resolved. Turn the cube over so that the first layer is now at the bottom.

Step 2: Solving the Yellow Side (Keep the Yellow on Top)

1. One corner in correct spot

• We’ll now rotate the top layer to see if the colour scheme of the yellow corner pieces are in the correct spot in reference to the first layer.
• Here, we may encounter a couple of scenarios:
• Case 1 (Zero corners in the correct spot): If none of the corner pieces are in the right position, use U moves on the top layer to get at least one corner correct.
• Case 2 (One corner in the correct spot): If one corner is in the correct position, proceed to the ”SOLUTION” step below.
• Case 3 (Two corners in the correct spot): If two pieces are in the correct location, perform U/U’/U2 moves on the upper layer to ensure at least one piece is correct.
• Case 4 (Zero corner or always two in the correct spot): Sometimes we can come across a specific situation when two pieces diagonal from each other are always in the correct position or none of the pieces are in the correct spot; in this case, hold any piece on the front/right and apply the procedure described in the ”SOLUTION” section below.

Solution

Now with only one correct piece, hold that piece to your right or front and apply the algorithm U R U’ L’ U R’ U’ L until all the corners are in the correct spot. With this, all the corners will be correctly positioned.

2. All corners in the correct spot

• Now, check that the yellow corner on your right layer is still unsolved. Then, perform (R’ D’ R D) (R’ D’ R D) to see if the yellow is solved on top.
• If it remains unresolved, perform (R’ D’ R D) (R’ D’ R D) and it should be solved, or if its solved then rotate the top layer by U/U’/U2 moves and move a yellow corner that hasn’t been solved to the right/front layer, and execute (R’ D’ R D) (R’ D’ R D) until all yellow is solved.
• Please do not rotate the cube under any circumstances, and continue doing so until the full yellow is solved. This would complete the solution to the yellow colour.

Congratulations you have solved the 2×2 Rubik’s Cube!!

In summary, solving the 2×2 Rubik’s cube is fairly simple and involves only 2 steps namely, Solving the 1st layer and the bottom layer. It is indeed a very interesting puzzle which a Rubik’s Cube enthusiast can get started with when starting cubing as a hobby.

Facts on the 2×2 Rubik’s Cube:

• Larry D. Nicholas invented the 2×2 Rubik’s Cube in 1970. 
• The 2×2 Rubik’s Cube has fewer pieces than the standard 3×3 Rubik’s Cube, but solving it still requires understanding of related algorithms. 
• There are 3,674,160 possible combinations in the 2×2 Rubik’s Cube. 
• It’s a fun fact that a 2×2’s interior is actually a 3×3, with the centre and edge pieces hidden between the corner pieces. Additionally, one corner piece on a 2×2 is always locked, while the other parts move around it.

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