Difference between revisions of "Cardan Reduction"
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algs=144 (72 with mirrors)  algs=144 (72 with mirrors)  
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purpose=<sup></sup>  purpose=<sup></sup>  
* [[Speedsolving]], [[FMC]]  * [[Speedsolving]], [[FMC]] 
Revision as of 19:03, 15 March 2017


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 is completed.
Steps
 CR1:: 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:: 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.