Cardan Reduction
From Speedsolving.com Wiki
|
Cardan Reduction is a novel "LS/LL" approach developed by Matt DiPalma for methods that pre-orient edges before the last slot (ZZ, Petrus, Heise, CFOP with edge control). It features a particularly low case count and movecount, in comparison with conventional LS/LL approaches. "LS/LL" is in quotes because the solution is not discretized in that way. This variant leverages cancellations, statistically common cases, rotational symmetry, inverses, and reflections to efficiently reduce the cube to a commutator/conjugate.
Cardan Reduction has 3 steps after EOF2L-1 is completed.
Steps
- CR1:: Insert FR edge and create a U-layer 2x1x1 block.
- the U-layer pair has a fairly high likelihood (32/75) of solving itself while the FR edge is inserted
- if not, this can take an average of 8 moves to do manually
- pairs can be preserved during F2L to drastically reduce this movecount (see examples)
- CR2:: Solve the 2x1x1 pair, all edges, and a corner (72 cases, and their mirrors).
- AUF the 2x1x1 pair so it points over the FR edge
- if the pair is a clockwise pair (UR edge and URF corner)
- determine edge permutation (6 possibilities)
- determine destination of UFL corner (12 possibilities)
- apply alg from speadsheet
- if the pair is an anticlockwise pair (UF edge and URF corner)
- rotate y (so FR edge is in LF)
- determine edge permutation (6 possibilities)
- determine destination of UFR corner (12 possibilities)
- apply alg that is mirrored from spreadsheet
- CR3:: Solve the remaining 3 corners using a commutator/conjugate.