Cardan Reduction


Information

Proposer(s):

Matt DiPalma

Proposed:

2017

Alt Names:

CR

Variants:

CR+, Step 34 of Heise Method

Subgroup:


No. Algs:

144 (72 with mirrors) for CR2 substep

Avg Moves:

24.90 (for CR1, CR2 and CR3 substep)

Purpose(s):

^{}

Previous state:

F2L1 + EO cube state

Next state:

Solved cube state


Cardan Reduction is a novel "LS/LL" approach developed by Matt DiPalma for methods that preorient 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 EOF2L1 (F2L1 + EO) is completed.
Steps
 (CR1) F2L1 + EO cube state to F2L1C + EO + 2x1x1 block cube state : Insert FR edge and create a Ulayer 2x1x1 block.
 the Ulayer 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) F2L1C + EO + 2x1x1 block cube state to F2L1C + LL2C cube state : 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
 Algorithms can be found here.
 (CR3) F2L1C + LL2C cube state to Solved cube state : Solve the remaining 3 corners using a commutator/conjugate.
External links