ALGORYTMY PLL PDF
PLL is the acronym for Permutation of the Last Layer. Permutation of the Last Layer is the last step of many speedsolving methods. In this step, the pieces on the. Symmetric. F (R U R’ U’) (R U R’ U’) F’. Adjacent. (R U2 R’ U’) (R U2) (L’ U R’ U’ L). 2x2x2 PLL (inc. Ortega P2L). Diagonal. U Face Only PLLs. U & D Face PLLs. Megaminx OLL and PLL. Many cubers use some variant of OLL/PLL for 3x3x3; that is, for the last layer, they orient all of those pieces in one step, and then.
As a 2x2x2 Speedsolving Method The first stage of CLL for the 2x2x2 consists of completely solving one layer of the cube (both orientation and permutation) as in the Layer-By-Layer method. Then, using one of 42 algorithms (2 of which are PLLs), you solve the remaining orientation and permutation of the last layer (thus giving a 1 Look Last Layer). All the subsets mentioned orient and permute the U-Layer Corners at the same time. CLL is just for 2x2. COLL orients and permutes the corners while preserving the F2L and LL edge orientation. Roux users have their own set of COLL algs that doesn't preserve the LL and F2L called CMLL.
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N-PLL b Used in: Special thank you to Lance for his pictures and some of his info.
Megaminx OLL and PLL
G-PLL b Used in: G-PLL a Used in: If you learn this, it will give you a surprising boost in speed over LBL. Wiki tools Special pages.
G-PLL d Used in: Because your first layer is much easier, and your “PLL” is much faster than normal as well. Note that all of these algorithms are written in the Western notationwhere a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z. Page actions View View source History More.
R-PLL b Used in: Retrieved from ” https: A-PLL b Used in: I tried it out and they looked pretty nice, but it’s easy to mistake fuchsia for red, so I changed them to the more conventional orange.
If you have to permute pieces in just one layer, you can use ;ll normal PLL algorithm, but if you have to permute pieces in both layers, you get to use a much faster Ortega algorithm! Permutation of the Last Layer is the last step of many speedsolving methods. Firstly, the Rubik’s 2×2 is far too small to be speedsolved and the mechanism doesn’t allow for corner cutting.
2×2 Tutorial Ortega method – Cube-Tips
The Ortega method is actually a “corners first” 3×3 method, but it adapts algogytmy well to the 2×2 that most people just know it as a 2×2 method. Rubik’s 2x2s bear the Japanese color scheme yellow next to white which can make recognition more difficult.
U-PLL b Used in: R2 Altorytmy R’ U2 R2. U-PLL a Used in: A-PLL a Used in: J-PLL b Used in: Once again thank you lance for letting me use your pictures and some of your info.
PLL Algorithms – CFOP Speedcubing Cases – Wiki
Here’s how it works: OLL cube state Next state: If you like, try out all of the available algorithms for a case to see which one feels the fastest to you – the same algorithm may not be the fastest for everyone, and shorter algorithms are algorytmj always faster than longer ones. There are two main brands: One last difference is color scheme.
Pl u M2′ u2 M2′ u M2′. There are 21 PLLs 13 if you count mirrors and inverses as being the same and each one is named after a letter.
Make a white side, but not a white layer. M2′ u’ M2′ u2′ M2′ u’ M2′.
The permutation images on this page do not take this into account. Permute all the pieces at once! Not logged in Create algorytky Log in. R-PLL a Used in: The diagrams below are top views of where you want the pieces to go.
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A scrambled Pocket Cube
The Pocket Cube (also known as the Mini Cube) is the 2×2×2 equivalent of a Rubik's Cube. The cube consists of 8 pieces, all corners.
- 4World records
History[edit]
Solved versions of, from left to right: original Pocket Cube, Eastsheen cube, V-Cube 2, V-Cube 2b.
In March 1970, Larry D. Nichols invented a 2×2×2 'Puzzle with Pieces Rotatable in Groups' and filed a Canadian patent application for it. Nichols's cube was held together with magnets. Nichols was granted U.S. Patent 3,655,201 on April 11, 1972, two years before Rubik invented his Cube.
Nichols assigned his patent to his employer Moleculon Research Corp., which sued Ideal in 1982. In 1984, Ideal lost the patent infringement suit and appealed. In 1986, the appeals court affirmed the judgment that Rubik's 2×2×2 Pocket Cube infringed Nichols's patent, but overturned the judgment on Rubik's 3×3×3 Cube.[1]
Permutations[edit]
Pocket cube with one side tilted
Any permutation of the eight corners is possible (8! positions), and seven of them can be independently rotated (37 positions). There is nothing identifying the orientation of the cube in space, reducing the positions by a factor of 24. This is because all 24 possible positions and orientations of the first corner are equivalent due to the lack of fixed centers. This factor does not appear when calculating the permutations of N×N×N cubes where N is odd, since those puzzles have fixed centers which identify the cube's spatial orientation. The number of possible positions of the cube is
The maximum number of turns required to solve the cube is up to 11 half or quarter turns, or up to 14 quarter turns only.[2]
The number a of positions that require nany (half or quarter) turns and number q of positions that require n quarter turns only are:
n | a | q | a(%) | q(%) |
---|---|---|---|---|
0 | 1 | 1 | 0.000027% | 0.000027% |
1 | 9 | 6 | 0.00024% | 0.00016% |
2 | 54 | 27 | 0.0015% | 0.00073% |
3 | 321 | 120 | 0.0087% | 0,0033% |
4 | 1847 | 534 | 0.050% | 0.015% |
5 | 9992 | 2256 | 0.27% | 0.061% |
6 | 50136 | 8969 | 1.36% | 0.24% |
7 | 227536 | 33058 | 6.19% | 0.90% |
8 | 870072 | 114149 | 23.68% | 3.11% |
9 | 1887748 | 360508 | 51.38% | 9.81% |
10 | 623800 | 930588 | 16.98% | 25.33% |
11 | 2644 | 1350852 | 0.072% | 36.77% |
12 | 0 | 782536 | 0% | 21.3% |
13 | 0 | 90280 | 0% | 2.46% |
14 | 0 | 276 | 0% | 0.0075% |
The two-generator subgroup (the number of positions generated just by rotations of two adjacent faces) is of order 29,160.[3]
Methods[edit]
A pocket cube can be solved with the same methods as a 3x3x3 Rubik's cube, simply by treating it as a 3x3x3 with solved (invisible) centers and edges. More advanced methods combine multiple steps and require more algorithms. These algorithms designed for solving a 2x2x2 cube are often significantly shorter and faster than the algorithms one would use for solving a 3x3x3 cube.
The Ortega method,[4] also called the Varasano method,[5] is an intermediate method. First a face is built (but the pieces may be permuted incorrectly), then the last layer is oriented (OLL) and lastly both layers are permuted (PBL). The Ortega method requires a total of 12 algorithms.
The CLL method[6] first builds a layer (with correct permutation) and then solves the second layer in one step by using one of 42 algorithms.[7] A more advanced version of CLL is the TCLL Method also known as Twisty CLL. One layer is built with correct permutation similarly to normal CLL, however one corner piece can be incorrectly oriented. The rest of the cube is solved, and the incorrect corner orientated in one step. There are 83 cases for TCLL, however algorithms have not been generated for solving all of them.[8]
The most advanced method is the EG method.[9] It also starts by building a layer (in any permutation), but then solves the rest of the puzzle in one step. It requires knowing 128 algorithms, 42 of which are the CLL algorithms.
World records[edit]
Vicente Albíter of Mexico solving it in 1.55 seconds at the Mexican Open 2008
The world record fastest solve is 0.49 seconds, set by Maciej Czapiewski of Poland on 20 March 2016 at Grudziądz Open 2016 in Grudziądz, Poland.[10]
The world record average of 5 solves (excluding fastest and slowest) is 1.21 seconds, set by Martin Vædele Egdal of Denmark on 21 October 2018 at Kjeller Open 2018, in Kjeller, Norway, with the times (1.06), 1.09, (1.64), 1.47, and 1.07 seconds.[10]
Top 5 solvers by single solve[11][edit]
Name | Fastest solve | Competition |
---|---|---|
Maciej Czapiewski | 0.49s | Grudziądz Open 2016 |
Sameer Aggarwal | 0.51s | Puget Sound Spring 2019 |
Michał Rzewuski | 0.52s | Grudziądz Open 2016 |
Jody Jones | 0.53s | Koalafication Melbourne 2019 |
Abraham Torres Ortíz Aguirre | 0.54s | ArCubingFest 2018 |
Top 5 solvers by average of 5 solves[12][edit]
Name | Average | Competition |
---|---|---|
Martin Vædele Egdal | 1.21s | Kjeller Open 2018 |
Will Callan | 1.23s | CubingUSA Nationals 2019 |
Jiazhou Li (李佳洲) | 1.25s | Xi'an Cherry Blossom 2019 |
Advay Sant | 1.31s | Oculus Cube Open 2019 |
Zayn Khanani | 1.34s | ODU Big Blue Spring 2019 |
See also[edit]
- Rubik's Cube (3×3×3)
- Rubik's Revenge (4×4×4)
- Professor's Cube (5×5×5)
- V-Cube 6 (6×6×6)
- V-Cube 7 (7×7×7)
- V-Cube 8 (8×8×8)
References[edit]
- ^'Moleculon Research Corporation v. CBS, Inc'. Digital-law-online.info. Retrieved 2012-06-20.
- ^Jaapsch.net: Pocket Cube
- ^http://sporadic.stanford.edu/bump/match/morepolished.pdf
- ^Ortega method tutorial by Bob Burton
- ^What is Varasano?
- ^What is CLL?
- ^CLL tutorial by Christopher Olson
- ^What is Twisty CLL?
- ^Description of the EG method
- ^ abWorld Cube AssociationOfficial Results - 2x2x2 Cube.
- ^
- ^
External links[edit]
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Pocket_Cube&oldid=932081462'