How to Solve a 2x2 Cube?

Solving a 2x2 Rubik's Cube, often called the Pocket Cube, is a fun and accessible challenge that serves as an excellent introduction to cube solving. It's simpler than the 3x3 cube, typically requiring only a few intuitive steps and a couple of algorithms.

Understanding the 2x2 Cube Structure

The 2x2 cube consists of 8 corner pieces, unlike the 3x3 which also has edges and centers. This simplified structure means you only need to focus on positioning and orienting these corners.

Step-by-Step Guide to Solving Your 2x2 Cube

Most beginner methods for the 2x2 cube follow a two-phase approach:

Phase 1: Solving the First Layer (Often the White Face)

The goal of this phase is to complete one entire face (e.g., the white face) and correctly position the four corner pieces on that layer, ensuring their side colors align with the adjacent faces.

1. Choose a Base Face: Start by picking a color for your first face (e.g., white).
2. Find the First Corner: Locate a white corner piece and place it anywhere on the bottom layer. It's often easiest to hold it in the bottom-right-front position.
3. Match Remaining Corners: Find the other three white corner pieces. For each one:
   • Bring it to the top layer, directly above where it needs to go on the bottom layer.
   • Use intuitive moves (such as repetitive R U R' or R' D' R D sequences) to insert it into its correct spot, ensuring the white sticker is on the bottom and its side colors match the implied adjacent centers.
   • Tip: If a piece is on the bottom but oriented incorrectly, you might need to bring it to the top temporarily to re-insert it correctly.
   • Repeat this for all four white corners until the entire white face is solved and the first layer's side colors also match.

Phase 2: Solving the Last Layer (Orienting and Permuting)

Once the first layer is complete, flip the cube so the solved white face is on the bottom. Now, you'll work on the top layer, which will typically be the yellow face (opposite to white). This phase involves two main sub-steps: orienting the corners, then permuting them.

Sub-step 2a: Orienting the Last Layer Corners (OLL - Orientation of Last Layer)

The objective here is to get all the yellow stickers on the top face, regardless of their position relative to each other.

• Identify Mis-oriented Corners: Look at your top (yellow) face. Some corners might have yellow stickers on the side instead of on top.
• Apply the Orientation Algorithm:
  1. Hold the cube so that a mis-oriented corner (one that needs its yellow sticker on top) is in the front-right-top position.
  2. Perform a simple, repetitive algorithm, such as R' D' R D, until that specific corner has its yellow sticker on top.
     • As described in some solving tutorials, you will apply a sequence of moves, repeating "Over. Then we're going to repeat until this corner is solved. There we go it's solved." This ensures the current corner is correctly oriented.
  3. Do NOT rotate the entire cube during this step. Instead, once one corner is oriented, you'll rotate the top layer (U or U') to bring the next mis-oriented corner into the front-right-top position, and repeat the R' D' R D sequence until it's also oriented.
  4. Continue this process for all four corners until all yellow stickers are on the top face.

Sub-step 2b: Permuting the Last Layer Corners (PLL - Permutation of Last Layer)

After all yellow stickers are on top, the corners might still be in the wrong positions relative to each other. This step involves swapping them to their correct spots.

1. Analyze the Top Layer:
   • Look for two adjacent corners that are already in their correct places (their side colors match their respective faces). If you find them, place them at the back-right (with the correct sides facing back and right).
   • If no two adjacent corners are solved, perform the permutation algorithm once from any orientation, then re-evaluate. You should then find at least two adjacent corners that are correctly placed.
2. Apply the Permutation Algorithm:
   • Once you have two adjacent solved corners, place them at the back-right of your top layer. If not, perform the algorithm from any orientation.
   • A common algorithm to permute the last layer corners is R U' R U R U R U' R' U' R2.
   • Alternatively, another widely used algorithm for this step is (R' F R' B2 R F' R' B2 R2).
   • Execute the chosen algorithm. After performing it, the remaining corners should move into their correct positions. You may need to perform it once or twice.
   • Once this is done, the entire cube should be solved. As the tutorial notes, "And then we move on to the next. One. And repeat. And there it is then. That's the whole thing lastly."

Tips for Success

• Practice Regularly: The more you practice, the more intuitive the steps and algorithms will become. Muscle memory is key.
• Understand, Don't Just Memorize: Try to understand why each move affects the cube. This helps in improvising and troubleshooting.
• Patience is Key: Learning to solve a cube takes time and persistence. Don't get discouraged by initial difficulties.

By following these straightforward steps, you'll be able to solve your 2x2 Rubik's Cube efficiently and confidently.