leeo
Regular
Total number of 5-cycle edge algorithms
My combinatorics is rusty, but I had some time this weekend to investigate the following question: How many 5-cycle edge algorithms are there?
With some programming, I have a catalog of all 1760 3-cycle edge algorithms from following the BH edge 3-cycle forms. I (inefficiently) combined all 1760 3-cycle edge algorithms to all 1760 3-cycle edge algorithms and filtered the result to those that are simple 5-cycles. For this result I count 304'128 5-cycle edge algorithms.
If I restrict those to only one "buffer" lead position, say UB, I count 126'720
Finally, if I further restrict those where only one of two attached facelets is targeted from the buffer, such as FD or DF, I count 11'520. For example, UB -> FD -> UR -> UF -> UL -> UB (again) F' R U R' U' F2 D U' F' U' F D' U2 F'
So, is the idea of employing a five-cycle to speed up the blindfold edge solving feasible? How many separate optimal generator forms are there that do not twist the center faces? (to be "supercube safe").
My combinatorics is rusty, but I had some time this weekend to investigate the following question: How many 5-cycle edge algorithms are there?
With some programming, I have a catalog of all 1760 3-cycle edge algorithms from following the BH edge 3-cycle forms. I (inefficiently) combined all 1760 3-cycle edge algorithms to all 1760 3-cycle edge algorithms and filtered the result to those that are simple 5-cycles. For this result I count 304'128 5-cycle edge algorithms.
If I restrict those to only one "buffer" lead position, say UB, I count 126'720
Finally, if I further restrict those where only one of two attached facelets is targeted from the buffer, such as FD or DF, I count 11'520. For example, UB -> FD -> UR -> UF -> UL -> UB (again) F' R U R' U' F2 D U' F' U' F D' U2 F'
So, is the idea of employing a five-cycle to speed up the blindfold edge solving feasible? How many separate optimal generator forms are there that do not twist the center faces? (to be "supercube safe").