obelisk477
Veteran
What's the number of possible LS positions, disregarding pre-AUF? I can't figure out how to not double count AUF psotions, I always get confused
Cale S
Veteran
if the corner is in U, always bring it above the last slot
for cases where the corner is in place, it can be in one of 3 orientations, and the edge can be in place oriented, in place flipped, in U oriented, or in U flipped. One of these cases is solved so 3*4 - 1 = 11 cases with the corner in place
for cases where the corner is in U, it can still be in one of 3 orientations, and the edge can be in place oriented, in place flipped, or in any of the 4 U positions flipped or oriented. 3*10 = 30 cases with the corner in U
11 + 30 = 41
basically all these: http://algdb.net/Set/F2L
for cases where the corner is in place, it can be in one of 3 orientations, and the edge can be in place oriented, in place flipped, in U oriented, or in U flipped. One of these cases is solved so 3*4 - 1 = 11 cases with the corner in place
for cases where the corner is in U, it can still be in one of 3 orientations, and the edge can be in place oriented, in place flipped, or in any of the 4 U positions flipped or oriented. 3*10 = 30 cases with the corner in U
11 + 30 = 41
basically all these: http://algdb.net/Set/F2L
obelisk477
Veteran
Doh...I meant including LL CO and EO
Cale S
Veteran
so full OLS instead of LS?
you can use AUF for the cases with both LS pieces permuted, which there are 5 of
edge flipped, corner solved: put the only flipped or only oriented edge in front, then there are 3^3 = 27 CO cases, 54 total cases
edge flipped, corner oriented cw: put only flipped or only oriented edge in front, then still 3^3 = 27 CO cases, still 54 total
edge flipped, corner oriented ccw: yeah same thing again so 2 * 3^3 = 54 total cases
edge solved, corner oriented cw: 8 CO cases not including AUF, but now the edge cases are L, line, dot, and cross. Normally this would be 108 cases but you can use symmetries to reduce this. For cross cases, this is just a subset of CLS, which has 8 cases. Dot also has 8 cases. L has no rotational symmetry so it's just 27 cases. For line cases, place the CO first, and then you'll have either a vertical or horizontal line. However, for the CO case with 90 degree rotational symmetry, you only have 1 case, so there are 7*2 + 1 = 15 cases. The total is 8 + 8 + 15 + 27 = 58 cases
edge solved, corner oriented ccw: This is just the mirror of the last case so also 58.
The total of these is 54*3 + 58*2 = 278
For cases where you cannot AUF, it's a lot easier because it's just 8 EO cases and 27 CO cases for all 36 of them, which makes 36*8*27 = 7776
So the total for OLS is 8054
edge flipped, corner solved: put the only flipped or only oriented edge in front, then there are 3^3 = 27 CO cases, 54 total cases
edge flipped, corner oriented cw: put only flipped or only oriented edge in front, then still 3^3 = 27 CO cases, still 54 total
edge flipped, corner oriented ccw: yeah same thing again so 2 * 3^3 = 54 total cases
edge solved, corner oriented cw: 8 CO cases not including AUF, but now the edge cases are L, line, dot, and cross. Normally this would be 108 cases but you can use symmetries to reduce this. For cross cases, this is just a subset of CLS, which has 8 cases. Dot also has 8 cases. L has no rotational symmetry so it's just 27 cases. For line cases, place the CO first, and then you'll have either a vertical or horizontal line. However, for the CO case with 90 degree rotational symmetry, you only have 1 case, so there are 7*2 + 1 = 15 cases. The total is 8 + 8 + 15 + 27 = 58 cases
edge solved, corner oriented ccw: This is just the mirror of the last case so also 58.
The total of these is 54*3 + 58*2 = 278
For cases where you cannot AUF, it's a lot easier because it's just 8 EO cases and 27 CO cases for all 36 of them, which makes 36*8*27 = 7776
So the total for OLS is 8054
JustinTimeCuber
Legend
fine
PenguinsDontFly
Legend
my hair has been wet for like 10 hours. I think Chris' shampoo is working.
OLLiver
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The top 100 3x3 singles are about to all be sub 7!
shadowslice e
Legend
Just out of interest, how many of those are feliks? Half?
Berd
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He was talking about indervidual people.
Sajwo
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OLLiver
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Ok what year will all the top individual 100 singles be sub 6? I'm gonna say 2021
shadowslice e
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nvpendsey
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Sajwo
Veteran
Maybe late 2020?
guysensei1
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Did OLL parity and lost my grip and damaged the sticker in a rather interesting way...
Chree
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Okay, Wolverine.
guysensei1
Legend
Including parity, how many cases are there for solving the square-1 that's cubic with 1 alg? Would it be in the thousands?
shadowslice e
Legend
i think it would be 8!x8!/8/2 (rotations and Aufs)= ~46million
guysensei1
Legend
okay, how many algs for:
1) move all white to the bottom, all yellow to the top with 1 alg
2) solve everything with 1 alg
kliang9299
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So I have these transparent Aolong V2 force cubes and I'm curious, how much do you guys think they're worth? I'm thinking about selling them on the Buy, Sell, Trade forum eventually since I really only use the blue one. They aren't stickered but are all lubed and tensioned and mostly unused, only turned to see if the tensioning was good.
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