Solve the 3x3x2 Rubik’s Cube: A Comprehensive Guide

The 3x3x2 Rubik’s Cube, often called the Rubik’s Domino, is a fascinating puzzle that offers a unique challenge compared to the standard 3x3x3 cube. While it might appear simpler due to its fewer layers, solving it requires understanding different algorithms and applying them strategically. This comprehensive guide will walk you through the steps to solve the 3x3x2 Rubik’s Cube, providing detailed instructions and visual aids to make the process as clear as possible.

Understanding the 3x3x2 Rubik’s Cube

Before diving into the solution, let’s understand the anatomy of the 3x3x2 cube:

• Pieces: The cube consists of corner pieces and edge pieces. There are no center pieces that remain fixed in relation to each other as in a 3x3x3 cube. This is an important distinction.
• Layers: The cube has two layers, which makes it feel much smaller than a standard Rubik’s cube.
• Moves: We’ll use standard Rubik’s Cube notation to describe the moves.

Notation

Understanding the notation is crucial for following the algorithms. Here’s a breakdown:

• F (Front): The front face, turned clockwise.
• B (Back): The back face, turned clockwise.
• R (Right): The right face, turned clockwise.
• L (Left): The left face, turned clockwise.
• U (Up): The top face, turned clockwise.
• D (Down): The bottom face, turned clockwise.
• F’, B’, R’, L’, U’, D’: The respective faces turned counter-clockwise (prime).
• F2, B2, R2, L2, U2, D2: The respective faces turned 180 degrees.

Steps to Solve the 3x3x2 Rubik’s Cube

We’ll break down the solution into manageable steps:

1. Orient the Top Layer Corners
2. Permute the Top Layer Corners
3. Orient the Bottom Layer Corners
4. Permute the Bottom Layer Corners

Step 1: Orient the Top Layer Corners

The first step is to orient all the corners on the top layer correctly. By ‘orient,’ we mean having the colors on the top layer facing upwards. In other words, the top face should ideally consist of a single color. It is possible that the corners in the top layer are not oriented yet (the colors are not uniform), but they are already in the correct position. This means that they may be in the correct place, but the colors are not pointing in the right direction. This step corrects this.

Examine the top layer. If all corners are already oriented correctly (i.e., the top face is a single color), skip to Step 2. If not, you’ll need to use the following algorithm:

Algorithm 1: R U R’ U’

This algorithm rotates a corner piece on the top right of the top layer. If your cube is held so that the problem corner is in this position, then performing this algorithm will rotate this corner.

Applying the Algorithm:

1. Identify a corner piece on the top layer that needs to be oriented.
2. Hold the cube so that this corner piece is in the top-right-front (URF) position. This is the upper-right corner of the Front face.
3. Perform the algorithm R U R’ U’ until the corner is correctly oriented. You might need to repeat this algorithm multiple times (2-3 times is common). The other pieces may be messed up temporarily, but do not worry.
4. Once the first corner is oriented, rotate the U (top) face to bring another misoriented corner into the URF position.
5. Repeat the algorithm R U R’ U’ for this new corner, until it is oriented. Repeat this for the remaining corners of the top layer.
6. Continue this process until all the corners on the top layer are oriented correctly.

Important Considerations:

• While performing this algorithm, other pieces might become misaligned. Don’t worry about that; just focus on orienting one corner at a time. The misalignments will be corrected in the subsequent steps.
• It is possible that when you bring a new corner into the URF position, you rotate the top layer to do this. Rotating the top layer affects the other corners that you have already corrected. You might need to repeat the above algorithm more than once for certain corners.

Step 2: Permute the Top Layer Corners

In this step, we’ll focus on permuting (positioning) the corners on the top layer. This means ensuring that each corner piece is in its correct location, regardless of its orientation.

Algorithm 2: R B’ R F2 R’ B R

This algorithm cycles the front-top-right (URF), front-top-left (UFL), and back-top-left (UBL) corners of the cube. This means that it swaps these pieces with each other.

Applying the Algorithm:

1. Inspect the top layer and identify how many corners are in their correct position.
2. If all corners are correctly positioned, skip to Step 3.
3. If only one corner is in the correct position, hold the cube so that this correct corner is at the back-top-left (UBL) position.
4. If no corners are correctly positioned, perform the algorithm once. This will ensure that at least one corner is now in the correct position. Then hold the cube so that this correct corner is at the back-top-left (UBL) position.
5. Now perform the algorithm R B’ R F2 R’ B R. This will cycle the positions of the three corners.
6. Repeat the algorithm until all corners are correctly positioned on the top layer.

Step 3: Orient the Bottom Layer Corners

This step is similar to Step 1, but focuses on orienting the corners of the bottom layer. Orienting the bottom layer means ensuring that all the colors on the bottom layer are facing downwards. If the bottom layer is a single color, this layer is oriented correctly.

Algorithm 3: L’ U’ L U

This algorithm rotates a corner piece on the bottom right of the bottom layer. If your cube is held so that the problem corner is in this position, then performing this algorithm will rotate this corner.

Applying the Algorithm:

1. Turn the cube upside down, so that the bottom layer is now the top layer.
2. Inspect the top (formerly bottom) layer for corners that are not oriented correctly.
3. Hold the cube so that a misoriented corner is in the top-right-front (URF) position.
4. Perform the algorithm L’ U’ L U until the corner is correctly oriented.
5. Rotate the U (top) face to bring another misoriented corner into the URF position.
6. Repeat the algorithm L’ U’ L U for this new corner until it is oriented.
7. Continue this process until all corners on the top (formerly bottom) layer are oriented correctly.
8. Turn the cube back, so that the original top is on top again.

Step 4: Permute the Bottom Layer Corners

This final step involves permuting the corners of the bottom layer to their correct positions.

Algorithm 4: L’ B L F2 L B’ L’

This algorithm cycles the front-top-right (URF), front-top-left (UFL), and back-top-left (UBL) corners of the cube. This means that it swaps these pieces with each other.

Applying the Algorithm:

1. Turn the cube upside down, so that the bottom layer is now the top layer.
2. Inspect the top (formerly bottom) layer and identify how many corners are in their correct position.
3. If all corners are correctly positioned, the cube is solved! You’re finished.
4. If only one corner is in the correct position, hold the cube so that this correct corner is at the back-top-left (UBL) position.
5. If no corners are correctly positioned, perform the algorithm once. This will ensure that at least one corner is now in the correct position. Then hold the cube so that this correct corner is at the back-top-left (UBL) position.
6. Now perform the algorithm L’ B L F2 L B’ L’. This will cycle the positions of the three corners.
7. Repeat the algorithm until all corners are correctly positioned on the top (formerly bottom) layer.
8. Turn the cube back, so that the original top is on top again.

Tips and Tricks

• Practice Makes Perfect: The more you practice, the faster and more proficient you’ll become.
• Memorization: Try to memorize the algorithms to avoid constantly referring to this guide.
• Patience: Solving the cube can be frustrating at times. Be patient and persistent, and you’ll eventually succeed.
• Online Resources: Utilize online resources like videos and simulations to further enhance your understanding.

Conclusion

Solving the 3x3x2 Rubik’s Cube might seem daunting at first, but with a clear understanding of the steps and algorithms, anyone can master it. This guide has provided you with a comprehensive walkthrough to tackle this intriguing puzzle. Happy cubing!