Ortega 2x2 is the most popular way to solve the 2x2 cube faster once you can already solve it layer by layer. Instead of lots of small steps, you make one face, then orient the top layer (OLL), then permute both layers at the same time (PBL). That is 12 algorithms in total: 7 for OLL and 5 for PBL.
Find your case fast
Look at your cube from above and tap the picture that matches it to see how to solve it. Grey cells are stickers you can ignore.
This post is for anyone who can already solve the 2x2 with the layer-by-layer method and can read the notation R, U, F, R′, U2 (see the cube notation page if it is new to you). Every case has a picture: the left one shows the cube before the algorithm, the right one shows it after.
!A scrambled 2x2 Rubik's Cube, the starting point for the Ortega 2x2 method Photo: [Mike Gonzalez (TheCoffee) / Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Pocket_cube_scrambled.jpg), CC BY-SA 3.0
What is the Ortega method?
According to the SpeedSolving Wiki, it is a corners-first method. Jeffrey Varasano described a similar approach back in 1981, and Victor Ortega made it popular around 2000, so many people also call it the Varasano or Varasano-Ortega method. Today it is known mainly as an intermediate 2x2 method.
The three steps of Ortega:
- One face: make the whole white face, without matching the colours on the sides.
- OLL: turn the cube so the white face is on the bottom, then make the whole top face yellow. 7 cases, 7 algorithms.
- PBL: put all 8 corners in place on both layers at the same time. 5 cases, 5 algorithms.
Compared with the layer-by-layer method, you skip matching the side colours in step 1, and each later step needs just one algorithm instead of doing the same algorithm over and over.
Step 1: Make one face
Goal: the whole white face is one colour. The side colours do not have to match: any corner in the wrong spot gets fixed in the PBL step.
This is what makes Ortega faster: the white stickers only have to be on the right face, so this step is usually very short. According to the SpeedSolving Wiki, a face solved in the fewest possible moves takes under 4 moves on average and never more than 5. You do not need to reach that at first: just use the corner-inserting algorithms you already know, except you do not have to pick the corner that belongs in that spot.
Hold the white face on the bottom. Bring a white corner to the spot right above the empty slot at the front right, then follow the direction of its white sticker. In the pictures below, the white face is on the bottom, the white corners keep their colours and the yellow corners are greyed out.
White sticker on the right face: R U R′
See it in 3D, before and after
- You start with (input)
- After the formula
White sticker on the front face: F′ U′ F
See it in 3D, before and after
- You start with (input)
- After the formula
White sticker on the top face: R U2 R′ U′ R U R′
See it in 3D, before and after
- You start with (input)
- After the formula
Once you get the hang of it, try to plan the whole face during inspection, and practise making the face in colours other than white. Go for whichever face takes the fewest moves.
Step 2: OLL, make the whole top face yellow
Goal: the white face stays on the bottom and the whole top face turns yellow. Do not worry yet about which corner is where.
Look at the top: how many yellow stickers are on the top face, and which way the other yellow stickers are facing. Turn U so it matches one of the 7 pictures below, then do the matching algorithm. In the pictures, the yellow corners keep their colours and the bottom layer is greyed out. Many of these algorithms are like the 3x3 OLL algorithms but shorter, because the 2x2 has no edges and no centres (SpeedCube Australia).
Sune: one yellow sticker on top
The yellow sticker on top is at the front left. The front-right corner has its yellow sticker facing the front, the back-right one faces the right, and the back-left one faces the back.
R U R′ U R U2 R′
See it in 3D, before and after
- You start with (input)
- After the formula
Antisune: one yellow sticker on top, the other way round
The yellow sticker on top is at the back right. The front-left corner faces the front, the front-right one faces the right, and the back-left one faces the left.
R U2 R′ U′ R U′ R′
See it in 3D, before and after
- You start with (input)
- After the formula
H: two yellow stickers at the front, two at the back
No yellow stickers on top. The two front corners have their yellow stickers facing the front, and the two back corners face the back.
R2 U2 R U2 R2
See it in 3D, before and after
- You start with (input)
- After the formula
Pi: two yellow stickers on the left face
No yellow stickers on top. The two left corners face the left, the front-right corner faces the front, and the back-right one faces the back.
F R U R′ U′ R U R′ U′ F′
See it in 3D, before and after
- You start with (input)
- After the formula
U: two yellow stickers on top, two both facing left
The two right corners have their yellow stickers on top. The two left corners both have their yellow stickers facing the left.
F R U R′ U′ F′
See it in 3D, before and after
- You start with (input)
- After the formula
T: two yellow stickers on top, two facing opposite ways
The two right corners have their yellow stickers on top. The front-left corner faces the front, and the back-left one faces the back.
R U R′ U′ R′ F R F′
See it in 3D, before and after
- You start with (input)
- After the formula
L: two yellow stickers diagonal on top
The front-right and back-left corners have their yellow stickers on top. The front-left corner faces the front, and the back-right one faces the right.
F R U′ R′ U′ R U R′ F′
See it in 3D, before and after
- You start with (input)
- After the formula
Step 3: PBL, put both layers in place
Goal: yellow on top, white on the bottom, and all 8 corners in place. After this step the cube is solved, though you may need a small U or D turn to line the two layers up.
How to spot the case: count the "bars"
Look at each layer on the four sides. If the two stickers of the same layer on one side are the same colour, that is a bar. Each layer can only be in one of three states:
- Four bars: the layer is already right, just turn it to line it up.
- One bar: two corners next to each other need to swap (an adjacent swap).
- No bars: two corners diagonal from each other need to swap (a diagonal swap).
Put the states of the two layers together and you have the case. There are 5 different combinations, each with one algorithm. When the layer with the problem is on the bottom, you flip the cube so it is on top and use the same algorithm.
In the pictures below, all 8 corners keep their colours.
One bar on top, bottom layer already right
Turn U so the bar is on the left face, then do (this is the 3x3 T-perm):
R U R′ U′ R′ F R2 U′ R′ U′ R U R′ F′
See it in 3D, before and after
- You start with (input)
- After the formula
No bars on top, bottom layer already right
No need to turn U first (this is the 3x3 Y-perm):
F R U′ R′ U′ R U R′ F′ R U R′ U′ R′ F R F′
See it in 3D, before and after
- You start with (input)
- After the formula
One bar on top, one bar on the bottom
Turn U and D so both bars are on the front face, then do:
R2 U′ B2 U2 R2 U′ R2
- You start with (input)
- After the formula
No bars on either layer
The shortest algorithm in Ortega, with no need to turn U or D first:
R2 F2 R2
- You start with (input)
- After the formula
One bar on top, no bars on the bottom
Turn U so the bar is on the front face, then do:
R U′ R F2 R′ U R′
- You start with (input)
- After the formula
When the bottom layer is the problem: flip the cube
The three remaining cases are just the cases above upside down. Flip the cube (white face on top) so the layer with the bar, or the layer that is not right yet, is on top, then use the same algorithm from above. In the three pictures below, the white face is on top.
No bars on top, one bar on the bottom: flip the cube, turn U so the bar is on the front face, and do R U′ R F2 R′ U R′.
- You start with (input)
- After the formula
Top layer already right, one bar on the bottom: flip the cube, turn U so the bar is on the left face, and do the T-perm.
See it in 3D, before and after
- You start with (input)
- After the formula
Top layer already right, no bars on the bottom: flip the cube and do the Y-perm.
See it in 3D, before and after
- You start with (input)
- After the formula
In what order should you pick up Ortega?
- Make one face without matching the sides. No new algorithms, you just drop the habit of matching the side colours.
- PBL before OLL. While you do not know OLL yet, you can make the top face yellow with Sune as in the beginner's 2x2 guide, then use PBL. Start with R2 F2 R2 (picture below) and the T-perm.
[cube2 BDL BDR DFL DFR BLU BRU FLU FRU: z2 R2 F2 R2] 3. OLL last. You may already know Sune and Antisune; H, U and T are very short; leave Pi and L for the end.
Each time you add a new algorithm, scramble the cube, solve up to that step, and use the new algorithm only when you get exactly that case. If you are not sure about a move, check the cube notation page again.
Video
Want to see it in motion? The short video below from the J Perm channel on YouTube shows more of what this post covers. The video belongs to that channel and is embedded straight from YouTube.
Sources
Frequently asked questions
Is Ortega 2x2 harder than the layer-by-layer method?
A little, because you need to remember 12 algorithms instead of 3. In return, each step takes just one algorithm, so you use fewer moves and solve faster. You can add the algorithms bit by bit, because you can still solve the cube when you only know some of them.
Why does step 1 not need the side colours to match?
Because the PBL step swaps corners on both layers at the same time. Any white corner in the wrong spot gets fixed there, so in step 1 the white stickers only have to be on the bottom face.
Can Ortega be used on the 3x3?
There is a 3x3 version of Ortega: you solve the corners first and the edges after (SpeedSolving Wiki). Even so, today people use Ortega mostly for the 2x2.
What comes after Ortega?
Fast 2x2 solvers usually move on to CLL, where making the top face and putting the top layer in place are combined into one step, or EG, an even bigger set of algorithms. Get Ortega down solid before you switch.
Cover photo: Mike Gonzalez (TheCoffee) / Wikimedia Commons, CC BY-SA 3.0