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This is a copy of a write-up that I posted on speedsolving.com in December 2021. The goal was to demonstrate the similarity among various corner permutation first methods and advocate for merging them into a single method with a single name. This was successful, with Joseph Tudor suggesting the name CEOR in a reply to the thread.
Over the years in the community there have been attempts to finish 3x3 solves using only R and U moves or to create methods which work well for one handed use for the majority of the solve. This naturally leads to the idea of solving corner permutation before getting to the last layer. Taking it further, people have tried to find ways to use only R, r, and U moves throughout most of the solve. In order to do this it means solving corner permutation as early as possible. There have been several CP first methods proposed since the early years of the online community and CP incorporated into later stages of other methods. Almost all of the CP first methods that have been proposed create an EOCP 2x2x3 then end with the right side block and 2GLL. Below is a timeline of CP methods. For a good summary on the CP concept, check out Jaap's page. PapaSmurf also has a great video.
Gilles Roux's CP method idea
Gilles Roux's CP method idea
In 2003 Gilles Roux, in a reply to Ryan Heise’s EOLine and EOCross idea post, proposed a method with the steps of CPLine > Finish 1x2x3 > EO + 2x2x3 > RB > 2GLL. However, the idea didn’t go any further than an example solve. There wasn’t much confidence as shown by the “This method is useless for [speedcubing].” comment.
Scramble: B2 L2 F2 L B2 R2 F2 U' L2 R2 B' U2 B L2 U' D2 F' R2 F L2 R' B' L D2 U2
U B R' B2 D2 // CPLine
R u2 R' u' r2 // FB at Dl
u R' u R2 u' R2 // 2x2x3 edges
u U2 R' U R u // EO + add edges
U R U2 R2 U' R' U' R U2 R' // Right block
U' R U2 R' U' R U' R' U // 2GLL
ZZ
ZZ
In 2006, the ZZ method was released to the community. It isn't a CP first method, but it was the first developed method to have early CP incorporated and likely influenced some of the CP first methods. There have been a few proposals for CP at various points in the ZZ solve.
ZZ-d: EOLine > left side block > CP.
ZZ-e: F2L-1 > CPLS
ZZ-f: EOLine or EOCross > Complete a left and right side square > solve the final pair for one of the built squares while performing CP. Proposed by Grzegorz Łuczyna and is on ZZ's original website.
Additional ZZ CP discussions and proposals below:
Jun 2008: Arnaud van Galen and Lucas Garron ZZ-d
2009?: CPLS (now CPLC)
Jan 2009: Noob's Approach to ZZ-d
2012?: Stachu Korick's ZZ-d information
2012?: Stachu Korick's CPLS/2GLL information
Jan 2012: ZZ-Orbit (old)
Jan 2012: ZZ-Orbit (new)
Aug 2012: ZZ-porky v1
Jul 2013: ZZ-porky v2
Aug 2013: ZZ-f (basically porky v1)
Aug 2013: ZZ-Profane Koala
In modern ZZ, the only CP method that is considered useful in speedsolving is CPLS. Modern CPLS, developed in 2020, is different from the older CPLS in that the modern one solves CP from all last slot cases. The original CPLS used only a couple of last slot cases. Raven has developed two recognition methods and, with help from PapaSmurf, generated the algorithms. For recognition, one of the two main ways is to put the F2L corner at URF and use CxLL recognition by checking RDF > RBU > ULF then infer the third sticker in many cases. The other recognition method is to put the F2L corner at UBL and then check the remaining 3 U corners to determine the CP. If the F2L corner is already at DFR, you can just check any 3 U layer corners. CPLS is best used with the FR slot in every solve. It can be used with the other F2L slots, however recognition can be difficult from the back slots and the user also needs to learn new algorithms for each slot.
Check out Raven's CPLS document to find the algorithms, recognition, and to also learn about the theory.
Thanks to RedstoneTim for providing the ZZ timeline and links.
Noah's CP Block
Noah's CP Block
In 2012, Noah Arthurs proposed a CP method that is based around building a 2x2x2 first. The steps are:
Step 1: Build a 2x2x2 and place all D layer corners without worrying about their orientation. Except ensure that one of the corners that touches the 2x2x2 is oriented.
Step 2: Permute the U layer corners.
Step 3: Solve the two edges that go with the oriented corner from step 1.
Step 4: Finish the right side block.
Step 5: 2GLL.
Noah's CP Block 2.0
Noah's CP Block 2.0
In 2013, Noah Arthurs proposed a different CP method. One which resembles the steps of the idea Gilles Roux mentioned in 2003. The steps are:
Step 1: Solve FB on the left.
Step 2: Place the DFR and DBR corners without caring about their orientation then do CP.
Step 3: Orient all remaining edges while solving the DF + DB edges.
Step 4: Solve the right side block.
Step 5: 2GLL.
Noah later updated NCPB 2.0 to change step 1 to be CPLine and step 2 to be to add the FL and BL edges with the center. “New step 1 approach: 1a: Solve DBL and DFL while permuting the corners, place DL with a slice move when convenient. 1b: Place BL and FL along with the left center.” So the steps of NCPB 2.0 become:
Step 1: CPLine at DL.
Step 2: Place the FL and BL edges and the L center.
Step 3: Orient all remaining edges while solving the DF + DB edges.
Step 4: Solve the right side block.
Step 5: 2GLL.
Noah also proposed LEOR in the same thread. He took the CP aspect out of his own method to propose it as a new method.
“If 2GLL is not a worthy goal to work towards, then I guess we'd have to consider what the method would look like without the CP step.
1: Left Roux block
2: EO + Finish Petrus block
3: Right block
4: LL (OCLL/PLL or COLL/EPLL)
I guess the question to ask is whether that's better than Petrus.
Step 1: Roux Block vs 2x2x2
Step 2: Roux-style EO + Two edges vs 2x2x3 + Petrus EO
I'm probably biased, but to me it looks equal at the very least and likely better because of no rotations and much less awkward.”
Briggs
Briggs
In 2015, Joseph Briggs proposed a CP first method. The steps are:
Step 1: CPLine at DL.
Step 2: Place the FL and BL edges and the L center.
Step 3: Orient all remaining edges while solving the DF + DB edges.
Step 4: Solve the right side block.
Step 5: 2GLL.
This is essentially the same steps as NCPB 2.0.
Briggs 2 (B2)
Briggs 2 (B2)
In 2015, Joseph Briggs proposed another CP first method. It is kind of like a CP first Roux method.
Step 1: CPFB.
Step 2: 1x2x2 at dbR.
Step 3: Create the final pair for F2B. Insert this pair while orienting the U layer corners and also orienting the last six edges to be in the arrow state.
Step 4: LSE.
2GR
2GR
In 2017, John Li proposed a CP method, and a recognition system, with the following steps:
Step 1: Create and place the DL + DBL pair while orienting all edges.
Step 2: Complete CPLine by permuting all corners while placing the DFL corner.
Step 3: Solve the FL, BL, DF, and DB edges and their centers to complete a 2x2x3.
Step 4: Solve the right side block.
Step 5: 2GLL.
C2GR
C2GR
In 2017, Zbigniew Zborowski proposed a CP first method along with a recognition system. The steps are:
Step 1: CPLine at DL.
Step 2: Orient all edges while expanding to a 2x2x3 block.
Step 3: Solve the right side block.
Step 4: 2GLL.
YruRU
YruRU
In 2020, Yash Mehta proposed a CP first method and a recognition system with the following steps:
Step 1: CPLine at DL.
Step 2: Place the FL and BL edges and the L center.
Step 3: Orient all remaining edges while solving the DF + DB edges.
Step 4: Solve the right side block.
Step 5: 2GLL.
A technique of orienting a couple of edges while solving step 2 was also incorporated.
There was a controversy when the thread for this was posted. Many noticed that the steps are exactly the same as the Briggs method (which has the same steps as NCPB 2.0). This was brought to the attention of Yash Mehta. It was also brought up that it is the same as C2GR (which has the same steps as NCPB 2.0 and Briggs). However, these concerns were dismissed and it was claimed that it is an entirely new method with the primary reason being that the CP recognition system is different and better.
Later, in 2021, a statement from Yash Mehta in the Mehta Discord server says that YruRU is a CP recognition method and not a 3x3 solving method. The overall suggestion being that, although LEOR was derived from the Briggs method, the Briggs method wasn’t popular so the Briggs method should be called LEOR-CP. Then YruRU as a method gets to be the method that is LEOR-CP.
TruSRU
TruSRU
In 2021 Vincent Trang proposed a CP first method. It makes use of S moves along with the usual R, r, U, and u moves. The DL slot is kept open and edges are oriented while solving the DL edge after the DF and DB edges have been placed.
Step 1: Solve the DBL and DFL corners while permuting all remaining corners.
Step 2: Solve the FL and BL edges.
Step 3: Solve the DF and DB edges.
Step 4: Solve the DL edge while orienting all remaining edges.
Step 5: Solve the right side block.
Step 6: 2GLL.
CP Nautilus
CP Nautilus
In 2021 I proposed a CP first variant of Nautilus. Instead of orienting a lot of edges, the 2x2x2 at dbr is first solved. I may make a thread soon with more details. But the primary steps are below:
Step 1: CPFB. The standard CPLine then FL + BL edges is fine.
Step 2: 2x2x2 at dbr.
Step 3: Orient the remaining six edges while solving the DF edge using a single algorithm.
Step 4: Solve the last F2L pair.
Step 5: 2GLL.
LEOR
LEOR
LEOR isn’t a CP method. However, it is important for historical purposes to note here that the LEOR method was developed by taking the Briggs method and removing the CP aspect.
“I extracted Leor from Briggs with the idea "2GLL isn't really any better for 2H than ZBLL is, and CPFB is a lot harder than FB, so why not just do Briggs with normal FB?" thus "Leor CP" is quite literally Briggs.” – Arc, 2020
It is interesting that Arc directly says that LEOR CP is Briggs. One of the creators of LEOR theirself says that LEOR CP is Briggs. If the marketing for YruRU is that YruRU is LEOR CP and the Briggs name shouldn't be used because it wasn't popular, how should this be classified? Do we follow the opinion of one of the LEOR creators or do we follow someone else's opinion?
Summary: Looking at all of the above, most of the methods have the following steps:
Step 1: CPLine at DL
Step 2: Place the FL and BL edges and the L center.
Step 3: Orient all remaining edges while solving the DF + DB edges.
Step 4: Solve the right side block.
Step 5: 2GLL.
NCPB 2.0, Gilles Roux’s idea, Briggs, C2GR, and YruRU all have the same steps. Looking at the YruRU controversy, there were three fully developed methods with identical steps before it was proposed. The main difference is in the recognition systems among each and the small details of how and when the EO + DF + DB edges are solved.
My personal proposal: We should call all of the CPLine based EOCP 2x2x3 methods NCPB. Or have a generic name like CFOP. Then have various CP recognition methods available for this full 3x3 solving method. Noah Arthurs was the first to propose and develop the EOCP 2x2x3 idea. He also proposed the steps of CPLine, FL + BL edges, then EO + DF + DB edges. This is the primary form that people are currently using in the CP first method. Gilles Roux may have mentioned the idea once many years ago. But it is a similar situation to the ZZ method having a few prior proposers, but Zborowski being the one to develop it into a full method of its own. Noah Arthurs fully saw the potential, developed the method, developed a recognition system, proposed it to the community, and continued to suggest improvements. Not all of the CP methods would be grouped into NCPB. Only the ones that follow the CPLine > FL+BL > EO + DF + DB steps. Other methods would likely remain their own method. Additional points:
YruRU, C2GR, and any others become CP recognition methods and not 3x3 solving methods. They will be recognition methods for NCPB and any CP first method that doesn’t start with an EOCP 2x2x3.
Orienting a couple of edges while solving the FL and BL edges after CPLine will be a technique for NCPB.
The Gilles Roux variant of solving the DF + DB edges after CPLine then using U u R to orient all edges and solve the FL and BL edges would be added as a variant on the NCPB wiki page.
Any new CP recognition methods that are applied to NCPB wouldn’t make it a completely new method. It would be NCPB with “x” recognition method. Just as using one of the several ZBLL recognition methods doesn’t make ZBLL or ZZ become a different method.
Update LEOR on the wiki to have Noah Arthurs as a proposer (the first proposer). We would still keep Arc and Pyjam as proposers since they developed the method. Not only did he propose it himself, but LEOR originally came from the Briggs method which Noah Arthurs also proposed first.
Of course this is just my own opinion. However I do think it is the most logical out of all of the options. It doesn't make sense to have five or more different methods which follow essentially the same steps but just use a different CP recognition method.
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