Difference between revisions of "Cardan Reduction"

 
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|image=Crsvg.png
 
|image=Crsvg.png
 
|proposers=[[Matt DiPalma]]
 
|proposers=[[Matt DiPalma]]
|variants=none
+
|variants=CR+, Step 3-4 of [[Heise Method]]
|anames=Step 3-4 of [[Heise Method]]
+
|anames=CR
 
|year=2017
 
|year=2017
 
|subgroup=
 
|subgroup=
|algs=144 (72 with mirrors)
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|algs=144 (72 with mirrors) for CR2 substep
|moves=24.90 for LS/LL
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|moves=24.90 (for CR1, CR2 and CR3 substep)
 
|purpose=<sup></sup>
 
|purpose=<sup></sup>
 
* [[Speedsolving]], [[FMC]]
 
* [[Speedsolving]], [[FMC]]
 
|previous=[[F2L-1 + EO cube state]]
 
|previous=[[F2L-1 + EO cube state]]
|next=[[Solved_cube_state]]
+
|next=[[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''' 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.
+
Cardan Reduction has 3 steps after [[F2L-1 + EO cube state|EOF2L-1 (F2L-1 + EO)]] is completed.
  
 
== Steps ==
 
== Steps ==
* CR1:: Insert FR edge and create a U-layer 2x1x1 block.
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# ''(CR1)'' [[F2L-1 + EO cube state]] to [[F2L-1C + EO + 2x1x1 block cube state]] : 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
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#* 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
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#* 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)
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#* 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).
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# ''(CR2)'' [[F2L-1C + EO + 2x1x1 block cube state]] to [[F2L-1C + LL-2C 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
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#* AUF the 2x1x1 pair so it points over the FR edge
:* if the pair is a clockwise pair (UR edge and URF corner)
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#* if the pair is a clockwise pair (UR edge and URF corner)
::* determine edge permutation (6 possibilities)
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#** determine edge permutation (6 possibilities)
::* determine destination of UFL corner (12 possibilities)
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#** determine destination of UFL corner (12 possibilities)
::* apply alg from speadsheet
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#** apply alg from speadsheet
:* if the pair is an anticlockwise pair (UF edge and URF corner)
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#* if the pair is an anticlockwise pair (UF edge and URF corner)
::* rotate y (so FR edge is in LF)
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#** rotate y (so FR edge is in LF)
::* determine edge permutation (6 possibilities)
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#** determine edge permutation (6 possibilities)
::* determine destination of UFR corner (12 possibilities)
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#** determine destination of UFR corner (12 possibilities)
::* apply alg that is mirrored from spreadsheet
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#** apply alg that is mirrored from spreadsheet
* CR3:: Solve the remaining 3 corners using a commutator/conjugate.
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#* Algorithms can be found [https://docs.google.com/spreadsheets/d/1S2HBejqM94xVjPdF9p4pklRc1qOidJ1IbMF-uYv9E3c here].
 
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# ''(CR3)'' [[F2L-1C + LL-2C cube state]] to [[Solved cube state]] : Solve the remaining 3 corners using a [[commutator]]/[[conjugate]].
  
 
== External links ==
 
== External links ==

Latest revision as of 22:48, 5 November 2017

Cardan Reduction
Crsvg.png
Information
Proposer(s): Matt DiPalma
Proposed: 2017
Alt Names: CR
Variants: CR+, Step 3-4 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: 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 (F2L-1 + EO) is completed.

Steps

  1. (CR1) F2L-1 + EO cube state to F2L-1C + EO + 2x1x1 block cube state : 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)
  2. (CR2) F2L-1C + EO + 2x1x1 block cube state to F2L-1C + LL-2C 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.
  3. (CR3) F2L-1C + LL-2C cube state to Solved cube state : Solve the remaining 3 corners using a commutator/conjugate.

External links