Ideas

Below are some additional ideas that I hope to one day get to. Or things that I have started and want to eventually finish.

1. Equatorial Polar: CPFB > Orient corner LR stickers to LR > EOLR for L9E > Permute all using <U2, R, r, M>. This combines a few thoughts.

   1. Gilles Roux once stated that he tried many ways to get rid of CMLL so that he wouldn't have to learn the algorithms. 

   2. I've put a lot of work into DR speed solving ideas, such as Polaris, NMLL, and Polar LSLL. There's also a Nautilus variant of FB > 2x2x2 > Polar LXSLL > Permute using <U2, R U2 R', r U2 r', M' U2 M>

   3. I have developed iterative corner solving (CO then CP), which is completely intuitive. In this case, the corners only need to be oriented.

2. Iterative DR and Iterative LSLL: I previously developed Iterative Corner Solving, where the corners are iteratively oriented then permuted like the edges of Roux LSE. Applying this to the U and R layers after the CPEO2x2x3 step in a method such as CEOR, we can iteratively solve the rest:

   1. Use quarter turn sequences from <U, R> to orient corners while positioning edges. There are two possibiltiies. Orient corners so that the U and D stickers are oriented, and solve the FR and BR edges. Or orient the LR stickers to LR and solve the UF and UB edges. This step is equivalent to Roux step 4a and 4b, with the LR corner orientation option more closely matching.

   2. Reduce and solve from here like Roux step 4c. R U2 R' U2 (M' U2 M U2), U2 R2 U2 (U2 M2 U2), R2 U2 R U2 R (M2 U2 M' U2 M'), U2 R2 U2 R U2 R2 U2 R (U2 M2 U2 M' U2 M2 U2 M') align with the 4c permutation step visually and in the turns that are required.

This idea can be combined with the Equatorial Polar idea to do CPFB > EOStripe with any two edges and any center > LR oriented DR > Solve with <U2, R, r, M>.

Corner permuted LSLL can be solved in a similar way:

1. Use quarter turn sequences from <U, R> to orient corners a certain way while partially positioning edges. (Equivalent to Roux step 4a <U, M>)

2. Use <U, R U2 R'> to finish orienting the corners to LR and finalize edge positioning. (Equivalent to Roux step 4b <U, M' U2 M>)

3. Permute all using <U2, R U2 R'>. (Equivalent to Roux step 4b <U2, M' U2 M>)

3. AI Recognition: I have put a lot of work into recognition methods for CxLL, ZBLL, and others. Something I've wanted to do for a long time is to compile the patterns then run it through a computer to find the optimal places to check stickers or the blocks to be on the lookout for. This may result in a recognition method that doesn't necessarily focus on an orientation then a pattern, sort of like Straughan. I wonder if it would end up being a combination of object + position based Straughan recognition where the fewest or best stickers are used within the visible stickers of the UF and UR bars.

4. Deterministic BLD: It would be interesting to develop a program that could determine the best sequence of cycles. Ones that lead to skipping cycles at the end because the solved state was reached early, the best ergonomics, or best move count. Maybe these optimal paths could even be human achievable through the creation of some flow charts or pattern determination and memorization.

5. Method Database: A database to hold algs for all methods, and not just the popular ones. Has features such as:

   1. Tags to make organizing algs easier. 1LLL, CLL, CMLL. Some sets work with multiple methods so the tags help with that.

   2. Sorting based on user like count, move count, or MCC.

   3. Integrated solver with the ability to click "generate new algs" for a single or multiple selected algs. Can input the desired move sets.

   4. User profiles with custom versions of the alg lists - their preferred algs. The ability to create new types of alg sets in their profile and share links to alg sets. People can share their profiles.

6. Megaminx

   1. APB: Get to the final two sides and build a three piece block of a corner and two edges at the back right. This leaves two unsolved corners and two unsolved edges within the bottom layers of the right side. Then use one algorithm to place the bottom corners while orienting all edges, use an algorithm to solve the remaining three pieces of the bottom layers (last corner and two edges, LXS), then solve the last layer.

7. UL5C: Solving L5C in one step requires memorizing 614 algorithms. But I believe that number can be greatly reduced if we take the concept of SL5C, which solves to a few possible states and not just the solved state, and combine it with the algorithm unions concept. This means that we would have several groups of L5C cases that have their own single algorithm that solves them to one of the desired states. This results in many cases having duplicate possible algorithms, reducing the number of algorithms required to be memorized. We may potentially see a reduction of 614/4 where we would have groups of four cases with one algorithm each. Even a reduction of 614/2 would be a major improvement. In December 2024 I tested the case count in my Union Creator program. It showed that UL5C can be done using 175 algs.

8. L7EOLR: I have this idea mentioned on the L7E page since it is the natural upgrade over my L7E system. The basic idea is that The FR or UR edge will be solved while orienting the remaining edges and placing the last two L/R edges on the bottom layer. Then finish the edge permutation. Additional tricks could be used with the edges. I think this and UL5C are what will transform the 1x2x3 > 1x2x2 > L5C > L7E method into something very appealing to use.

9. L5E to solve LSE: Something I keep considering is the possible recognition of the five visible edges in Roux LSE then applying the shortest or fastest L5E algorithm to set up the five edges to a good continuation to finish LSE.

10. ACMLL: ACMLL should be run through a program to find all possible block configurations, their ACMLL algorithm quality, and the best ACMLL sets to learn. I think I have identified most of the best sets on the ACMLL page, but I would like to see the idea put into a program to find everything.

11. LSLL: I have had a couple of ideas for continuing from the LSLL state. These are written with oriented edges LSLL in mind, but can also be applied to non-oriented LSLL.

    1. Bipod: Use algorithms to solve either a 1x2x3 on the U layer or a 1x2x2 on the U layer and the dFR pair. At first it may seem like it would be an insane number of algorithms and would be complex. But consider what happens when the FR edge is on the U layer. There are now three U layer edges on the U layer. From this point, all that needs to be done is to solve the two corners that belong with those three edges and cycle the edges if necessary. An add-on is to permute the remaining two edges. This leads to L3C as the final step. This significantly adds to the algorithm count. A workaround to always have an L3C ending but without the additional algorithms is to have a U layer edge at UR and perform an R turn to move it to BR. Now solve two corners around any three edges while cycling those edges if necessary. The final U layer edge will be automatically permuted, leaving an L3C state.

    2. States Reduction: Another idea is to recognize the LSLL state and use an algorithm to reduce to states that have good algorithms or intuitive endings. Examples include R U' R', R U2 R', Sune, etc. This is essentially Petrus 270 or Duplex pulled back to LSLL.

12. RX2: This is an idea and discovery that I made maybe sometime around 2010. It is a 2x2 method where the corners are solved like Roux LSE. It turns out that the corners truly can be treated like edges and do have a very similar appearance. When thought of in this way, and looking at the last step, it kind of looks like, for example, the UFL and UFR corners are the result of some kind of cell division where they were originally an edge, but was split into two corners. Other move sets besides what is described below can be used. For example, say you have a bar of corners on the bottom left or on 3x3 have a 2x2x3 on the bottom left and the corners are permuted as in CEOR. You can orient and permute the corners LSE style using R and U turns.

    1.  Orient the corners using x rotations and U turns (equivalent to M and U and step 4a of LSE).

    2. Permute the corners into bars using x rotations and U turns (equivalent to M and U and step 4b of LSE). This is moves like x U2 x, the same as M' U2 M' to solve the L/R edges.

    3. Permute the bars using x rotations and U2 (equivalent to M and U2 and step 4c of LSE).

13. Straughan and ATCRM L5C Recognition: It would be nice to create the pseudo recognition for L5C when using Straughan style or ATCRM.

14. Additional 2x2 Methods: I have a lot of other ideas for 2x2 methods. Here is a post about some ideas.

    1. Polar 2x2: Place the bottom layer corners with the L/R stickers on L/R then use an algorithm to solve the U layer corners and correct the bottom layer. The first step gives more possibilities at the start than EG and creating this first step requires fewer moves, but the method overall requires more algorithms since there are more sets.

    2. OD: Create a first layer that has a bar from the U layer at DR. Then solve the corners that are on the U layer while correcting everything.

15. Elo rating system: Some sports have a rating system that ranks players and also attempts to predict the winner of a match. A similar system could be created for cubing using the WCA database.

16. Crazy thoughts: Sometimes I have abstract thoughts about something that may be a possibility. Sometimes it even turns out to be possible and leads to a new concept. RX2 above is an example where I was thinking about a possible <x, U> move set on 2x2x2 and thought it would be a crazy concept if the 2x2x2 could be solved like Roux LSE.

    1. Hybrid DR: Is there some way to set up states on the U and R layers that are a merge of UD and LR DR states. Maybe the Ul block is in the UD DR state and the dR block in the LR DR state. Something like U' L U' R U L' R' U2 R U R' U'. In this case, the corners can be solved in LR DR and the edges can be solved in UD DR. But can this be taken further with parital UD or LR DR anywhere in any mixture in U and R? What about extending this idea to the entire cube to have a UD, FB, and LR DR around the cube?

    2. Quarter Turn DR: Is there a way to treat quarter turns as half turns, creating a new way of solving that is like DR but for quarter turns? A scramble is provided in my Deterministic Solving article that may be an example: U' R' U' R' F' U' R U2 L F U2

    3. Piece Type Transfer: Can we solve the 3x3x3 U and D layers using 5x5x5 center solving techniques? What about using big cube edge solving techniques to solve the 3x3x3 corners? Maybe techniques from one piece type of many other puzzles can be transferred to different piece types of different puzzles.