Straughan Recognition

Straughan recognition is a recognition concept to be applied to various steps and puzzles. Up to now, there has been a common recognition style among the various steps in methods. This typically involves first checking the orientation of all pieces then checking additional stickers to complete the recognition. But with Straughan recognition, the minimum number of required stickers is checked. For CLL, for example, it turns out that only four total stickers are needed to determine a case. For ZBLL, just six are required. Straughan recognition is a versatile system that is useful for many steps and puzzles and has applications for tracking and prediction. Because of the low sticker count, this system may work well for one looking solves. It is also a completely unique style of recognition. Other recognition systems are based on checking an orientation then a relational pattern. Straughan recognition is instead purely location based.

The recognition takes advantage of the fact that we can know the state of unseen pieces just by looking at those currently visible. Pieces of the cube are connected kind of like quantum entanglement. If a corner is twisted on the last layer, that means that there must be at least one other corner twisted. If certain stickers of three corners are checked, the identity of the fourth, unseen, corner is known. This recognition system takes advantage of this property to allow for checking the minimal amount of information.

When I chose Roux as my main 3x3 method in 2006, I didn't know how to recognize CMLL. Gilles Roux's website didn't provide a recognition system, instead presenting cases in a table showing orientations and swaps. So I developed an intuitive system of first checking the U sticker orientation then knowing the side sticker order around the U layer and checking those to intuitively determine the permutation. Gilles Roux later told me about the common CO + 3-4 sticker pattern recognition method and I switched to that. Around 2021 I started trying to apply the NMCLL / ATCRM concept to early corner permutation to create a pattern based system. I wasn't able to work it out at the time.

In April and May 2024 I took another look, trying to create an LR + FB orientation or UD + LR or FB orientation combination recognition method for early corner permutation. While looking into it, I got sidetracked and started thinking about my old CMLL recognition method, wondering if there was some way to refine it into something better. Drilling down into that thought path led me to realize that through deduction and process of elimination just four stickers are necessary to determine a CMLL case. I started development of a spreadsheet with the initial idea to check any two matching or opposing F/B (or L/R) stickers on UBR and UFR then any matching or opposing two L/R (or F/B) stickers on UFR and UFL then intuitively determine the swaps. I eventually realized that it can be further simplified to checking any two adjacent colors, then further to always checking the same two adjacent colors.

This discovery not only resulted in a new way to recognize CMLL, but also an entirely new recognition concept for all steps. It even allowed for the development of a new way to recognize early corner permutation, solving the initial problem that got me thinking about my original CMLL recognition method and led to this new recognition system.

Advantages

• The minimum required stickers are checked, so no additional effort or time spent.

• Great for case tracking, prediction, and one looking entire solves.

• Versatile - can be used with CLL, ZBLL, TCLL, corner permutation steps such as CPLine or CPLS, and numerous other steps and puzzles.

• No new patterns among CLL, TCLL+, and TCLL-. The patterns that are in CLL are the same in TCLL. There is no need to memorize and practice new patterns for each of the corner sets. This is unlike U sticker based orientation where TCLL+ and TCLL- require memorizing and practicing 86 new patterns. With Straughan recognition, along with good look ahead and prediction, there are no new awkward recognition cases.

• Works well with pseudo. Whether used with non matching blocks or in a method such as 42, the recognition still works with minimal changes.

• Can be thought of as a three sticker tracking system for CLL. Only one sticker needs to be tracked on the corner with two stickers.

Disadvantages

• Each algorithm is associated with four patterns when learning. Using Straughan recognition with CLL involves learning 162 patterns.

• The recognition isn't meant for in the moment recognition as with U sticker based recognition. Straughan recognition is intended for tracking and prediction before arriving at the step.

The base four sticker system as applied to 2x2 has been developed for CLL, EG, TCLL, and LS. It also works for other 2x2 methods. Currently in 2x2 solves using U sticker based recognition, numerous stickers are checked and traced during inspection. Ultimately, 3 or 4 stickers are tracked but at least three U stickers are are also checked as part of the process to know to which corners those final 3 or 4 stickers belong. With Straughan recognition there is no need to check additional stickers. Only four total are checked and tracked, which should be a slightly faster process.

Click to View 2x2 Algs Document 

Using four sticker recognition as the base, ZBLL can be recognized using just six stickers. For ZBLL on big cubes, the adjacent permutation parity can be avoided in one of a few ways.

1. One way is to use the alternate version of the recognition that searches for opposite edges, such as red and orange.

2. Another way is to find the opposite edge of one side. For example, instead of red and blue, find red and green or blue and orange. Pretend that the opposite edge is one of the normal edges and the algorithm will solve to opposite parity. This technique requires knowing whether or not there will be a permutation parity issue.

3. A final way is similar to the previous method. Instead of finding an opposing edge, know which algorithm will solve the current edge configuration to opposite parity. There are three algorithms available for each ZBLL case to solve to opposite parity. So there is a choice among a few algorithms to use your favorite. Just like the technique above, this requires knowing that two edges are swapped.

1LLL works similar to ZBLL, but includes one additional edge sticker, making a total of seven stickers. The RU, FU, and LU stickers, for example, are all that are needed to complete the full last layer edge identification.

For OLLCP, the four CLL stickers and any three edge stickers will provide all of the necessary information.

It may also be interesting and useful to have a combination recognition for last layer methods. Instead of finding the six or seven specific stickers, just the four sticker CLL part of the recognition can be used. Then, add in recognition of visible edges and where they are relative to the CLL pattern. This could be useful when only the four CLL stickers were tracked during the final moves of solving the first two layers.

Click to View ZBLL Document

The same four sticker recognition for CLL can be used for the Roux method's CMLL step. It can also be applied to Roux advancements such as ACMLL.

Click to View CMLL Document

For two sided PLL recognition, only five of the six stickers are necessary. One sticker from each of the three corners and the two edge stickers. Along with checking patterns, knowledge of the colors order around the last layer is also necessary to distinguish cases. For PLL prediction, just three corner stickers are necessary to know the current corner permutation. If two visible R/F/L/B edge stickers are seen quickly enough, that provides the complete permutation information.

The document below provides two recognition styles. One for impromptu recognition - intended for use when arriving at PLL and during OLL for short term prediction. And another for one looking solves during inspection - tracking the five specific stickers that belong at FLU, FU, FUR, RU, and RUB or FLU, FU, RFU, RU, and RUB. Or another group of working five stickers depending on your preference or the scramble.

Click to View PLL Document

I have applied this system to early corner permutation, as seen in the CEOR method or the early corner permutation version of Nautilus. Instead of the tracing method that existed before, this new system uses only the location of certain stickers. The same system can be used with CPLS or any other step that permutes corners before the last layer.

Click to View Early Corner Permutation Recognition Document

This system can also be applied to the 42 method. The 42 method contains two main variants. One is full L5C. With L5C, only the D sticker of the DFR corner needs to be added in to create a five sticker recognition system for L5C. The other main variant of 42 uses CCMLL. Four sticker recognition can be used for CCMLL with some additional rules.

Steps for 2x2, 3x3, and other puzzles will eventually be developed. For example, this system can be applied to OLLCP or Kilominx / Megaminx CLL (five stickers) or L6C (six stickers).

The base four sticker CLL recognition can also be used during pseudo, such as after solving a pseudo layer or face on 2x2, non-matching blocks in a 3x3 method such as Roux, or CCMLL from the 42 method.

One option is to use the F and R stickers. Then, learn the single sticker that changes at the FUR position for each type of non matching block. You should know the kind of block you built and therefore will know the sticker to search for.

Another option is to always use the left side stickers for recognition. In this style, the sticker that changes is instead one that isn't part of the corner with two stickers.

In this option, you learn the adjacent matching sticker type that should be together depending on the U corner that is on the bottom layer. Then add in the white sticker from the bottom layer to complete the four sticker recognition. The single yellow sticker can be used instead of the white sticker.

This option is more complicated than the first option. Instead of knowing a simple corner pair as in the first option, stickers to search for are memorized. The corner with two stickers is always the same, but the other two stickers will be different.

The four stickers used in the various documents aren't the only ones that are possible. There are several other possibilities as shown below. The use of two colors was chosen for simplicity.

Sometimes a case can be recognized using just three stickers instead of the standard four.  The final sticker can sometimes be automatically deduced, without checking any other positions. The corner with two stickers has specific positions for the two stickers. If only one of the stickers on the two sticker corner is currently visible within the current AUF, seeing the other matching sticker on another corner can help deduce the location of that sticker or it can be ignored and not included as part of the recognition.

In the following example, the two red stickers are visible, but two of the other stickers on those corners aren't. The blue sticker at URF helps narrow down the case. The location of the fourth sticker, the second blue sticker, can be deduced from the fact that there is no blue sticker at UBR. There can't possibly be a blue sticker at UFL if the corner is the yellow red blue corner due to the fixed sticker order. There also can't be a blue sticker at BRU because of the same sticker order. Because there isn't a blue sticker at UBR for this case, that must mean that the second blue sticker is at LUF. Technically this is still a four sticker system because in the example UBR is checked, but it is a useful technique for narrowing down cases.

It can also be known from a specific orientation set where the second sticker is on the two sticker corner. For example, when the two right side stickers are oriented, the second sticker will always be in one of four positions. Notice in the following images that the blue sticker only has four possible positions.

Knowing the corner sticker order, the orientation sticker location possibilities, and where stickers can appear within each case set can help narrow down a case even more quickly. Eventually a deduction document will be developed or the techniques added to each case set. These deduction techniques apply not only to CLL, but also to last layer with edges included and other steps.

Straughan recognition is meant to be paired with tracking to ensure that there is little or no recognition time when arriving at the step.  However, if only two of the corners were tracked, the remaining sticker may be out of view. To avoid having to AUF to find the sticker, other stickers can be checked. Usually this will preserve the four sticker concept, but sometimes it may mean having to check two additional stickers, for a total of five.

Currently the cases are organized based on the location of a single set of stickers then the remaining stickers make up the subcases. Other styles of organizing the stickers are possible and are all still Straughan recognition. Some examples include:

1. Orientation then permutation.

2. Any set of matching stickers as the base.

3. The orientation of the two sticker corner.

4. Shape based, like OLL.

The current organization was chosen for simplicity and for providing a target set of stickers to track during the final pair. It also works well with pseudo. Other organization styles likely have their own benefits. The first one in the above list is interesting because it should be possible to learn the intuitive swaps similar to 3 sticker recognition on distinct sticker puzzles and know the AUF based on the orientation within. The orientations can be associated with an invisible and unnecessary to be checked U sticker orientation, in a way reducing the patterns from 162 to 42.

Four stickers is the minimum for identifying a CLL case. Breaking it down, three U stickers among three corners can determine orientation, but can't determine permutation on their own. For permutation, side stickers must be involved. Three side stickers among three corners aren't enough to determine the full permutation or the full orientation. This is because of the doppelganger effect. If two red stickers are involved, the two red corners need to be differentiated by checking an additional sticker on one. If one red, one blue, and one orange are used, each of those have doppelgangers. Because of the doppelganger effect, a sticker needs to be added to the three for full CLL case identification.

This can be compared to the four U edges when corners are unsolved. Three edge side stickers can determine orientation. Three can also determine permutation. Three total can completely identify the case. All of the edge side stickers are unique and so there are no doppelgangers. Two adjacent corners can be seen as an edge divided into two like cell division. The two end up sharing the same two original colors, but then have different end point colors.

A set of rules can be developed:

1. Must involve at least three corners.

2. Must involve at least three side stickers.

3. When the four stickers are on three corners

   1. There must be a pair of matching side stickers.

   2. Two stickers must be on one of the two matching corners and can be any two stickers.

   3. The fourth sticker must be one of the two colors adjacent to the two matching side stickers.

4. When the four stickers are on four corners, they must be four unique side stickers.