2×2, Beginner and Ortega Methods
The 2×2 puzzle consists of eight corner pieces, like a 3×3 with no edges or centers. It shares notation with the 3×3 puzzle, minus slice and double layer rotations. Link to 3×3 notation.
Beginner Method
If you know how to solve a 3×3, you can solve a 2×2 without learning anything new.
- Solve the bottom layer by positioning and orienting the four D corner pieces. Use your intuition or the corner algorithms from the 3×3 beginner method in Part One of the Solve It! Guide.
- OLL—Orient the four U corner pieces using either the Solve It! Beginner method or the seven corner algorithms from 2-look OLL.
- PLL—Permute the four U corner pieces. Again, you can use either the Solve It! Beginner method or the two corner algorithms from 2-look PLL.
Ortega Method
The Ortega Method is a faster solution for the 2×2. Here’s an overview of the steps.
- Orient the D side without positioning/permuting the corners.
- OLL—Orient the last layer.
- PBL—permute both layers.
Let’s look at each step in detail.
Step 1—Orient the D Side
In the first step, orient the four D side corner pieces, which should be faster than correctly permuting them. For maximum speed, strive for texture independence; that is, be able to use any side as your D side. During the 15-second inspection, look for a pair, in which two adjacent corners have the same texture, and use that as your D side. With some practice, you’ll be able to orient the remaining D side textures with only a few quick rotations.
Before proceeding to step 2, examine the arrangement of the bottom layer. Note whether the corners require an adjacent corner swap, a diagonal corner swap, or are already correctly permuted. If you have an adjacent corner swap, note the direction of the headlights. With practice, you can predict the bottom layer arrangement during inspection.
Step 2—OLL
These algorithms will be familiar to anyone already solving the 3×3 with CFOP. Because the 2×2 has no edge pieces, some OLL algorithms are simpler than their 3×3 analogues.
Ortega 1–SUNE:
R U R′ U R U2 R′
Ortega 2–ANTISUNE:
R U2 R′ U′ R U′ R′
Ortega 3–Pi
Setup: same
Solution: F R U R′ U′ R U R′ U′ F′
Note: This is an F rotation, two sexy moves, and a final F′.
Ortega 4—U
Setup: F R U R′ U′ F′ U2
Solution: F R U R′ U′ F′
Ortega 5—L
Setup: repeat twice.
Solution: F′ R U R′ U′ R′ F R
Orient with U side of back-left corner pointing left.
Ortega 6—T
Setup: repeat twice.
Solution: R U R′ U′ R′ F R F′
This is the sexy move (R U R′ U′) followed by sledgehammer (R′ F R F′). Orient with top of T shape at left.
Ortega 7—H
Setup: same
Solution: R2 U2 R U2 R2
Orient with headlights facing front and back.
Step 3—PBL
In the final step, perform a single algorithm to correctly permute the top and bottom layers simultaneously, then perform an AUF (additional U face) rotation is necessary. In Step 1, you examined the arrangement of the bottom layer corners. Start step three by examining the arrangement of the top layer corners. Then perform the algorithm appropriate for the two arrangements. There are five algorithms for five scenarios.
- One layer is solved, the other layer requires an adjacent corner swap.
- One layer is solved, the other layer requires a diagonal corner swap.
- Both layers require diagonal corner swaps.
- Both layers require adjacent corner swaps.
- One layer requires an adjacent corner swap, the other layer requires a diagonal corner swap.
Each of the following algorithms are named (bottom layer)/(last layer). For example, in Ortega 8a, the bottom layer is solved, and the last layer requires an adjacent corner swap.
Ortega 8a—solved/Adjacent
Orient your cube with headlights facing left. Any adjacent corner swap algorithm from 1-look PLL will solve this scenario. However, most 2×2 cubers prefer to use the second J-perm.
Setup: R U R′ F′ R U R′ U′ R′ F R2 U′ R′ U′
Solution: R U R′ F′ R U R′ U′ R′ F R2 U′ R′
Ortega 8b—Adjacent/Solved
This is a variant of 8a that avoids the expense of an x2 reorientation.
Setup: R U R′ F′ R U R′ U′ R′ F R2 U′ R′ U′ x2
Solution: R′ U R′ F′ R U R′ U′ R′ F R2 U′ R′ U′ R2
Ortega 9—Solved/Diagonal
Any diagonal corner swap algorithm from 1-look PLL will solve this scenario. However, most 2×2 cubers prefer to use the Y-perm.
Setup: same
Solution: F R U′ R′ U′ R U R′ F′ R U R′ U′ R′ F R F′
Ortega 10—Diagonal/Diagonal
Setup: same
Solution A: R2 F2 R2
Solution B: x R2 U2 R2
The second solution is useful if you find U2 easier than F2. The initial x reorientation can be done implicitly.
Ortega 11—Adjacent/Adjacent
Orient with headlights facing back.
Setup: same
Solution A: R2 U′ R2 U2 F2 U′ R2
Solution B: y2 L2 U′ L2 U2 y R2 U′ y R2
Solution B demonstrates the case in which headlights are pointing front. It avoids reorienting the cube with an initial y2. As you practice it, perform the intermediate y reorientations implicitly.
Ortega 12—Diagonal/Adjacent
Orient with the last layer headlights facing front.
Setup: same
Solution: R U′ R F2 R′ U R′