Difference between revisions of "Cardan Reduction"

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{{Substep Infobox
{{Substep Infobox
|name=Cardan Reduction
|name=Cardan Reduction
|proposers=[[Matt DiPalma]]
|proposers=[[Matt DiPalma]]

Revision as of 16:49, 14 March 2017

Cardan Reduction
Proposer(s): Matt DiPalma
Proposed: 2017
Alt Names: Step 3-4 of Heise Method
Variants: none
No. Algs: 144 (72 with mirrors)
Avg Moves: 9.07
Previous state: F2L-1 + EO cube state
Next state: Solved_cube_state

F2L-1 + EO cube state -> Cardan Reduction step -> Solved_cube_state

The Cardan Reduction step is the step between the F2L-1 + EO cube state and the Solved_cube_state.

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.


  • 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.

External links