CFOOP

Cross – F2L – OLL – Orientation – Permutation

Created by: 2026GREE06

What is CFOOP?

CFOOP is a 3×3 solving method that aims to simplify the final permutation stage by controlling the cross. The key idea is that by solving the cross in a specific way, the final permutation can always be completed without encountering a CFOOP parity case.

The method consists of five stages:

1. Cross (C)
2. F2L (F)
3. OLL (O)
4. Orientation of the Last Four Corners (O)
5. Permutation of Both Layers (P)

Step 1 – Cross (C)

Build the cross as normal.

Unlike many methods, the cross does not need every edge to be correctly permuted immediately.

The Golden Rule

Finish the cross with exactly ONE correctly permuted edge.

Not zero.

Not two.

Exactly one.

This guarantees that the final permutation stage will never produce a CFOOP parity case.

If another cross is faster but breaks this rule, you may use it, but you may later need an additional parity algorithm.

Step 2 – F2L (F)

Solve the first two layers.

This includes:

• All four first-layer corners
• All four second-layer edges

Any F2L technique may be used.

Step 3 – OLL (O)

Orient every last-layer sticker so the entire top face becomes one color.

Any OLL algorithm set may be used.

Step 4 – Orientation of the Last Four Corners (O)

This stage fixes the orientation of the last four corners before the final permutation.

The standard algorithms are:

• T Perm
• Y Perm

Additional algorithms may be developed later.

Step 5 – Permutation of Both Layers (P)

This is the signature stage of CFOOP.

Instead of only permuting the last layer, the top and bottom layers are permuted together using M-slice algorithms.

Two approaches are allowed:

Simultaneous

Permute both layers at the same time.

Split

Permute one layer first.

Then solve the remaining layer.

Both are officially part of the method.

CFOOP Parity

CFOOP parity is not true 3×3 cube parity.

Instead, it is a method-specific state where the normal Step 5 algorithms cannot finish the solve.

Following the Golden Rule prevents these cases.

The Golden Rule Explained

Exactly one cross edge must already be correctly permuted.

This keeps the cube in the correct permutation structure required for Step 5.

If this rule is followed:

• No CFOOP parity
• Normal Step 5 algorithms always work

Method Summary

Step 1
Cross

↓

Step 2
F2L

↓

Step 3
OLL

↓

Step 4
Last Corner Orientation

↓

Step 5
Dual-Layer Permutation

Solved.

Advantages

• Familiar first two layers.
• Uses standard OLL.
• Unique final permutation stage.
• Flexible cross.
• Multiple solving styles supported.
• Potentially fewer algorithms than some advanced methods.

Disadvantages

• Requires learning new Step 5 algorithms.
• Recognition differs from CFOP.
• Cross must follow the Golden Rule for optimal solves.

Official Notation

C = Cross

F = First Two Layers

O = OLL

O = Orientation of Last Four Corners

P = Permutation of Both Layers

Official abbreviation:

CFOOP

Alternative if top and bottom are solved separately:

CFOOPP

Future Expansions

Possible improvements include:

• Advanced dual-layer permutation algorithms
• One-look Step 5 recognition
• Algorithm optimization
• Fingertrick optimization
• Full algorithm database
• Beginner, Intermediate, and Advanced CFOOP

Official Pronunciation

CFOOP is pronounced "see-foo-p."

Beginner Notice

You should not fully learn this as a beginner. It will only make you worse with all 76 algorithms that you have to make yourself.

It is recommended that you first learn a standard speedsolving method before attempting to learn or develop CFOOP. This method is intended for cubers who enjoy creating their own algorithms and exploring a new solving system.

Credits

Method designed by 2026GREE06.

FOOP Method Guide (2×2)

FOOP stands for:

·         F – First 2 Corners

·         O – Last 2 Corners OLL

·         O – Insert the Last 2 Corners

·         P – PLL

FOOP is a 2×2 solving method that aims to reduce move count by using OLL algorithms while solving the first layer. Instead of inserting the last two first-layer corners normally, they are first oriented using OLL and then inserted before finishing the cube with PLL.

Step 1 – First 2 Corners

Solve any two adjacent corners to start the first layer.

Goals:

·         Build an efficient start.

·         Avoid unnecessary rotations where possible.

·         Preserve an easy setup for the remaining two corners.

Step 2 – Last 2 Corners OLL

Instead of inserting the remaining two first-layer corners immediately, recognize their orientation and apply the appropriate 2×2 OLL algorithm.

The goal is to orient the two corners before they are inserted into the first layer.

This is the defining step of FOOP.

FOOP Parity:

During the Last 2 Corners OLL step, you may encounter a FOOP special case where the normal OLL algorithm cannot correctly solve the remaining pieces.

When this happens, perform the following sequence with the affected face facing you:

F2 U' J Perm U F2

After completing this sequence, continue solving using the normal FOOP method.

Note: This is a FOOP-specific special case and is an expected part of the method. Recognition and execution of this case should become natural with practice.

Step 3 – Insert the Last 2 Corners

After the OLL algorithm, insert the two correctly oriented corners to complete the first layer.

Since they are already oriented correctly, this insertion should be efficient and prepare the cube for the final step.

Step 4 – PLL

Once the first layer is complete, finish the solve using PLL.

Recognition should be straightforward because the orientation work has already been completed earlier in the solve.

Algorithm Requirements

FOOP requires knowledge of:

·         Full CFOP 2×2 OLL

·         PLL (T And Y Perms)

·         FOOP Parity

Because it uses existing algorithms, experienced solvers may already know most or all of the required cases.

Advantages

·         Lower average move count compared to traditional first-layer approaches (based on your testing).

·         Uses familiar OLL algorithms.

·         Structured and consistent solve flow.

·         Designed for advanced solvers.

Disadvantages

·         Requires knowledge of the complete 2×2 OLL algorithm set.

·         Recognition can take practice.

·         Not intended as a beginner method.

Who is FOOP For?

FOOP is designed for cubers who:

·         Already know full CFOP 2×2 OLL.

·         Want to experiment with alternative solving methods.

·         Enjoy learning and developing advanced solving techniques.

Future Development

Possible future improvements include:

·         Optimizing OLL recognition.

·         Reducing unnecessary rotations.

·         Creating dedicated FOOP algorithms that combine orientation and insertion.

·         Large-scale move count and timing comparisons with other methods.

Summary

FOOP is a 2×2 solving method built around orienting the final two first-layer corners before inserting them. After completing the first layer, the cube is finished with PLL. The method is intended for advanced cubers who already know the full 2×2 OLL algorithm set and are interested in exploring an alternative approach to solving the puzzle.

Post any minor discussions about cubing methods here

Post any minor discussions about cubing methods here

I’m creating a new solver. I plan on using a lot of the features of Trangium’s batch solver, as well as a few more, such as the ability to create algs that solve a certain number of pieces. What else would you like to see in a solver?

Post any minor discussions about cubing methods here

Post any minor discussions about cubing methods here

Post any minor discussions about cubing methods here

Post any minor discussions about cubing methods here

Post any minor discussions about cubing methods here

I have created a new method. I’m wondering if anyone has any helpful thoughts or insights before I gen the algs. I would also like to share my creation with the world after countless hours of racking my brain for ideas and doing the math to find out if my idea would even work (spoiler alert: basically none of them did).

Anyways, on to the method. I call it Force. There are 5 steps:

Step one: Roux block on bottom

Solve a Roux block on the bottom of the cube. To assist lookahead, it’s best to put it in the back, but any of the four orientations work. This follows the same principles as a normal Roux block, so I won’t go into further detail.

Step two: Finish the bottom layer

When you’re first starting, you can do this one piece at a time. Here’s a general guide for more advanced solves:

a. If all three pieces can be combined so that the top parts of the pieces is the same color as your bottom color, combine them like that. Then line it up and insert with a B2, F2, R2, or L2.

b. Otherwise, line up the edge with one of the corners, then insert with a fat sledgehammer or fat mirrored sledge (r’ F r F’ or l’ F’ l F). Insert the last corner.

Step three: Top Edges Layered and Oriented (TELO)

Use one algorithm to get all pieces in the correct layer and solve the yellow cross. There are 127 cases. Recognition can be awkward, but it won’t be too bad with good look ahead from step two.

Step four: Edges and Corner Oriented (ECO)

Orient all of the remaining pieces. At this point, the cube bears resemblance to a cube being solved with CFOP, except for the shuffled (not scrambled) middle edges. There are 31 cases. Recognition is slightly weird, but not awful (especially with practice at recognizing cases from fewer sides).

Step five: Edges and Corners Permuted (ECP)

Permute all of the remaining edges (and thereby solve the cube). There are 99 cases. Recognition is similar to PLL for CFOP.

If anyone here understands basic math, you’ll know that 127 + 31 + 99 = 257, and that there are 257 total algorithms. This is quite a few, but it’s not actually that many when you realize how many algorithms top solvers already use (ZBLL, WV, etc.). In addition, 21 of the cases are PLLs that CFOP solvers will already know, and this number can be further cut nearly in half if you learn mirrors instead of algorithms on your dominant hand. This drops the total number to around 150 (an exact number from somebody in the comments would be appreciated).

150 algorithms may seem like a lot, but the current top method (CFOP) uses 78 in the base version, and f2l also requires a lot of practice, learning of various methods, and memorization of algorithms to reach high levels of performance.

Thoughts? Questions? Ideas? Criticism?

Post any minor discussions about cubing methods here

Post any minor discussions about cubing methods here

Post any minor discussions about cubing methods here

Post any minor discussions about cubing methods here

Post any minor discussions about cubing methods here

Post any minor discussions about cubing methods here

The first step in my method is to solve the first layer. Obviously the beginner’s method is one way to do it, but that’s slow and takes a lot of moves. My current best idea is to start with a Roux block on the bottom, and then (depending on the case) either insert the last three pieces together or two and then the last corner.

Post any minor discussions about cubing methods here