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.

• Union Creator: I developed a program for solving to any desired state, not just the solved state. This is useful for things like algorithm unions as seen in CLL+1. The program works, but I have very little programming experience and so it runs too slowly to be useful. There are a few possible reasons for this.

  1. Finding the possible unions among the cases turns out to be an example of something called the Set Cover Problem. Isolating this part of the code, it doesn't seem to be too slow, but I'm not yet 100% certain. I have an upgraded version of the union finding code that isn't on the site yet.

  2. My code for creating the table for the cases and the cases that the algs can solve to may not be fast enough.

  3. Everything is done at once after the click of a single button. Maybe splitting the union finding from the cases and coverage table causes a lot of slowdown. I'm thinking to have a separate button for unions after the cases and coverage table has been generated.

  4. A combination of the above.

• 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. 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.

• 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.

• 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.

• 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).

• ATCRM L5C Recognition: It would be nice to create the pseudo recognition for L5C.

• Pattern Corner Permutation (PCP): Currently the way of recognizing early corner permutation in methods like CEOR is to use a tracing system. I think there exists a way to do it using patterns. Using the opposite stickers concept from NMCMLL / ATCRM and finding all of the L/R (or F/B) stickers on the corners provides a lot of permutation information. Then add in a few additional stickers and you should know the necessary swaps.

• 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.