What Is the Petrus Method? Solve a 3x3 Cube in 5 Steps

What is Petrus?

The method is named after Lars Petrus, a cuber from Sweden. He used it to become Swedish champion and to finish fourth at the first World Championship in Budapest in 1982 (Lars Petrus, Wikipedia). The SpeedSolving Wiki gives 1981 as the year the method was created (SpeedSolving Wiki).

The big idea behind Petrus: when you solve layer by layer, you keep having to break up and rebuild the parts you have already finished. With Petrus you build one big block first, and after that you only turn the faces that do not touch it (Lars Petrus).

Petrus has five steps:

1. A 2x2x2 block in one corner of the cube.
2. Grow it into a 2x2x3 block.
3. Fix the edges: every remaining edge has to be "oriented" (facing the right way).
4. Finish the first two layers using only R and U.
5. The last layer.

How to read the pictures

• Yellow on top, white on the bottom, green at the front. The left face is red and the right face is orange.
• The 2x2x3 block sits at the bottom left: the bottom two layers of the red side. The two faces that stay free are yellow (top) and orange (right).
• Each picture shows two cubes: on the left is before the moves, on the right is after. Pieces you do not need to care about in that step are coloured grey.

Every move sequence in this post was tested on the EasyRubic cube simulator. If R, U and R' are new to you, see Rubik's Cube notation for beginners.

Step 1: The 2x2x2 block

A 2x2x2 block is one corner, three edges and the three centres around them. In this post it is the bottom-back-left corner: the white-red-blue corner.

There is no fixed algorithm for this step. An easy way for beginners: put the white-red and white-blue edges around the white centre, then join the corner with the red-blue edge to make a pair and bring the whole pair in.

In the picture below, the two white edges are already in place and the last corner-edge pair is up on the top layer:

U L U' L'

Lars Petrus thought this is the step that needs the most practice, because every scramble is a new puzzle (Lars Petrus). Try lots of ways and pick the one with the fewest moves.

Step 2: Grow it into a 2x2x3 block

Add three pieces to the front of the 2x2x2 block: the white-green edge, the white-red-green corner and the red-green edge. The result is the bottom two layers of the red side, plus the white edges at the front and back.

First bring the white-green edge to the bottom front. In the picture below, that edge is at the top front, and the move F2 (turning the front face half a turn) brings it down:

Then join the corner with the red-green edge to make a pair and put it into the front-left slot:

U' L' U L

The SpeedSolving Wiki notes that for each position of the 2x2x2 block, there are three directions you can grow it in (SpeedSolving Wiki). In this post, the block always grows towards the front.

Step 3: Fix the edges

This is the step that makes Petrus special. There are seven edges left to solve. Each one is either oriented (facing the right way) or misoriented (facing the wrong way). A misoriented edge can never reach its right spot if you only turn R and U, so you have to fix it first.

Spotting a misoriented edge

For each edge, pick one sticker to look at:

• An edge with yellow or white: look at the yellow or white sticker.
• An edge with no yellow or white: look at the green or blue sticker.

Then:

• An edge in the top or bottom layer is oriented if that sticker is on the top or bottom face.
• An edge in the middle layer is oriented if that sticker is on the front or back face.

Any edge that does not pass is misoriented. Lars Petrus points out that the number of misoriented edges is always even, so you can always fix them in pairs (Lars Petrus). Handy bonus: R and U never turn an oriented edge into a misoriented one or the other way round, so you can use R and U to move the bad edges to a comfy spot.

Fixing two bad edges in three moves

Put the two bad edges at top right and middle right at the front, then do:

F' U F

1. You start with (input)
3. After the formula

The F' move pulls part of the 2x2x3 block out for a moment, but the last F puts it back in one piece.

If the two bad edges are at top left and middle right at the back, use the back face instead of the front:

B U B'

1. You start with (input)
3. After the formula

With four or six bad edges, fix them one pair at a time. Lars Petrus notes that the two, four and six edge cases each have their own fastest fix (Lars Petrus); once you get the hang of it, you can look into those.

Step 4: Finish the first two layers with only R and U

From here on you only turn R and U. These two faces do not touch the 2x2x3 block, and they never make an edge misoriented again. Lars Petrus warns: if you turn another face by mistake, misoriented edges come back and you have to redo step 3 (Lars Petrus). He also suggests holding the 2x2x3 block firmly in one hand and not changing your grip.

What is left is the bottom two layers of the orange side: the white-orange edge at the bottom, and two corner-edge pairs at the back and the front.

The white-orange edge only needs R or R2 to get in place. The picture below shows the back pair going into the back-right slot:

U' R' U R

The last pair goes into the front-right slot:

U R U' R'

With only two faces to turn, this step is quicker on the hands than free block building. The SpeedSolving Wiki mentions one downside: after step 3 you often have to turn the whole cube once to hold it more comfortably (SpeedSolving Wiki).

Step 5: The last layer

Thanks to step 3, all four top edges are already oriented. Once the first two layers are done, you always see a yellow cross on top without doing anything extra. All that is left is the corners and the positions of the edges.

According to the SpeedSolving Wiki, the last layer can be done in several ways: orient the corners then permute everything (OCLL and PLL), solve the corners then the edges (COLL and EPLL), or solve the whole layer in one go with ZBLL (SpeedSolving Wiki). Beginners should start with the three small steps below, which need only a few algorithms.

5a. Twist the corners so yellow faces up

If only one corner has yellow on top, put it at the front left. This is the Sune algorithm:

R U R' U R U2 R'

The Antisune algorithm is the Sune run the other way round, and it also uses only R and U:

R U2 R' U' R U' R'

For any other case (no corners or two corners with yellow on top), do the same as the yellow face step in the 7-step guide: use the Sune, look again, and repeat until all four corners have yellow on top.

5b. Swap the corners

Look for two corners next to each other that share the same colour on one side face. If you find a pair like that, put it on the left and use the algorithm below to swap the two corners on the right:

R U R' U' R' F R2 U' R' U' R U R' F'

If there is no such pair, two diagonal corners need to swap:

F R U' R' U' R U R' F' R U R' U' R' F R F'

These two algorithms do use F, but they do not make any edge misoriented. They may swap some of the top edges around, and the next step puts those back in order.

5c. Swap the edges

If one edge is already in place, put it at the back. The other three need to cycle round. One way:

R U' R U R U R U' R' U' R2

The other way:

R2 U R U R' U' R' U' R' U R'

If no edge is in place, do either algorithm above once and one edge will be in place. When this step is done, the cube is solved.

What is good about Petrus, and what is hard?

Pros:

• Fewer moves. The SpeedSolving Wiki estimates about 45 moves when you use ZBLL for the last layer, fewer than CFOP (SpeedSolving Wiki).
• Fewer algorithms. The first two layers are done by thinking. The last layer needs anywhere from 2 to 493 algorithms depending on the way you pick, according to the SpeedSolving Wiki.
• You never break what you have built. This is why Lars Petrus gave up on solving layer by layer (Lars Petrus).

Cons:

• Block building is hard to do in few moves, especially for beginners.
• Block building is less comfortable for your fingers, even once you know finger tricks (SpeedSolving Wiki).
• Few people use it and there are few guides. The SpeedSolving Wiki says Petrus used to be the second most popular method after CFOP, but fewer people have used it since CFOP, Roux and ZZ took over.

How to get started with Petrus

1. First be able to solve the cube with the beginner's method. If you cannot yet, start with the 7-step guide.
2. Practise the 2x2x2 block. Scramble the cube, build only the 2x2x2 block, then scramble again. Count your moves and try to bring the number down.
3. Practise growing it into a 2x2x3 block until you no longer need to think for long.
4. Practise spotting misoriented edges before you turn. Petrus and ZZ both use this skill.
5. Reuse the last layer algorithms you already know. The Sune, corner swap and edge swap above are enough to solve the whole cube.

To compare Petrus with other methods, see Rubik's Cube methods, What is CFOP? or the Roux method.

Sources

• Petrus method (SpeedSolving.com Wiki)
• Solving Rubik's Cube for speed (Lars Petrus)
• Step 3: Twist the edges (Lars Petrus)
• Step 4: Finish 2 layers (Lars Petrus)
• Lars Petrus – Wikipedia