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.

• 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. Expanding upon this, 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>)

The LSLL version is actually equivalent to L5E instead of Roux LSE. To really translate Roux LSE, it should be applied to the U and R layers as a whole.

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*, R2> to finish orienting the corners to LR and finalize edge positioning. (Equivalent to Roux step 4b <U, M* U2 M*, M2>)

3. Permute all using <U2, R* U2 R*, M2>. (Equivalent to Roux step 4b <U2, M* U2 M*, M2>)

• PCP Alternate: The original idea behind PCP around 2021 or 2022 was to check corner orientations. For example, the orientation of the LR stickers and the UD stickers together forms a unique corner case. This is like the original NMCLL recognition from 2004. Applying this recognition system to the U and R corners, or all eight corners, will show whether there is a swap and the location of the swap. If applied to all eight corners, the best swap or the starting cube orientation where no swap is necessary can be found. Really the current PCP method should be part of the Straughan recognition concept and this alternate idea should be called PCP.

• FTO CFOP: In addition to Nautilus for FTO, I have also proposed CFL (Centers, F2L, LL) as a method that is like CFOP. First the BL, F, D, and BR centers are solved, then the F2L triples are solved, then the last layer can be solved in one or two steps. Here is an example solve.

• Megaminx

  • 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.

• 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.

• 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.

• 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.

  • 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.

  • 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.

• 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.

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

  • 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.

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

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

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

  • 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.

  • 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.