Difference between revisions of "Cardan Reduction"
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{{Substep Infobox | {{Substep Infobox | ||
|name=Cardan Reduction | |name=Cardan Reduction | ||
− | |image= | + | |image=Crsvg.png |
|proposers=[[Matt DiPalma]] | |proposers=[[Matt DiPalma]] | ||
− | |variants= | + | |variants=CR+, Step 3-4 of [[Heise Method]] |
− | + | |anames=CR | |
|year=2017 | |year=2017 | ||
|subgroup= | |subgroup= | ||
− | |algs=144 (72 with mirrors) | + | |algs=144 (72 with mirrors) for CR2 substep |
− | |moves= | + | |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=[[ | + | |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)'' [[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) | |
− | + | # ''(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 | |
− | * CR3 | + | #* Algorithms can be found [https://docs.google.com/spreadsheets/d/1S2HBejqM94xVjPdF9p4pklRc1qOidJ1IbMF-uYv9E3c here]. |
− | + | # ''(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
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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
- (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)
- (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.
- (CR3) F2L-1C + LL-2C cube state to Solved cube state : Solve the remaining 3 corners using a commutator/conjugate.