Speedsolving.com Wiki - User contributions [en]

COLL

2009-08-17T11:56:08Z

Maarten95:

'''COLL''' (an abbreviation for '''Corners of Last Layer''') is a method in the [[CxLL]] group that solves the [[Last Layer]] [[corner]]s in one [[algorithm]], while preserving the [[F2L]] and the orientation of the LL [[edge]]s. So, after the COLL step, only edge permutation (EPLL) is left.

COLL is not to be confused with [[CLL]], which is an abbreviation for exactly the same name. The difference is that CLL preserves the F2L but not the edge orientation, so it leaves the LL edges scrambled and the next step would be full [[ELL]]. For some cases the CLL and the COLL are the same algorithm, but for other cases the CLL is much shorter. For CLL and COLL algorithms, see the page on [[CxLL Algorithms]].

One possible extension of COLL is [[ZBLL]]. This LL method solves the entire LL if the edges are already oriented, but it has almost 500 cases.

===See also:===
* [[CxLL Algorithms]]
* [[CLL]]
* [[CMLL]]
* [[ZBLL]]

[[Category:3x3x3 methods]]
[[Category:Cubing abbreviations and acronyms]]

ZBLL

2009-08-17T11:55:06Z

Maarten95:

'''ZBLL''' (short for ''[[Zbigniew Zborowski|Zborowski]]-[[Ron van Bruchem|Bruchem]] Last Layer'') is a step of a method which involves solving the entire [[last layer]] in one step, assuming that the [[edge]]s are already oriented. This is part of the [[ZB method]], but it can be useful for any other method which leaves the edges of the last layer oriented after F2L is solved (such as the [[Petrus method]]).

ZBLL indeed sounds like a very useful step to learn, but the main reason that it is not in wide use is that it involves a massive 177 algorithms (counting inverses and mirrors are the same), or a total of 493 cases. Only a handful of people have ever learned this step in its entirety. If you wish to learn it, it is useful to start by learning either [[OCLL]]/[[PLL]] or [[COLL]]/[[EPLL]], so that you will always be able to finish the cube relatively quickly even if you do not yet know the ZBLL case.

===Learning Approach===

The ZBLL cases are divided into 7 sets: T, U, L, Pi, Sune, Anti-sune, H, and the Pll cases, in which all pieces are oriented. The sets are then divided further into 40 subsets. They are recognized by their [[COLL]] case as well as a corresponding edge cycle. Every subset contains 12 cases, which are all different edge cycles possible with the COLL case of that set. Many people recognize ZBLL by looking at the UFR corner, and its neighboring stickers. Whether the stickers are adjacent, or opposite allows for a quick recognition. However, this method only works for the T, U and L subsets of ZBLL, because in the other cases the UFR corner is not correctly oriented. Another way to recognize is through blocks of colour or simply the edge cycle.

===Edge recognition===

For the T, U and L cases (there are 3*6*12=216 algorithms in this set) recognition goes as follows:

1. Recognize the orientation case.

2. Recognize the [[COLL]] case.

3. Recognize the edge cycle by looking at the UFR corner and the edge stickers around it.

4. Apply the corresponding algorithm.

Step 3 may look a little complicated, but it's actually not too bad. In total there's 12 cases, but those are recognized by 2 minor sub-cases, of which there are 3:

C: If the FU sticker is the same as the FRU sticker, and if the RU sticker is the same as the RUF sticker.

A: If the FU sticker is an adjacent color to the FRU sticker, and if the RU sticker is an adjacent color to the RUF sticker.

O: If FU and FRU are opposite, and if RU and RUF are opposite.

A case is recognized by the combination of those. First comes the FU/FRU relation, then the RU/RUF relation, divided by a slash. That means there are 9 possibilities with these cases: C/C, C/A, C/O, A/C, A/A, A/O, O/C, O/A, O/O. However, there are 12 cases. That's because the A case can mean 2 stickers. That's why the last 3 cases are known as C/OX, O/CX and OppX. This means that you don't look for the relation between FU/FRU and RU/RUF, but between FU/RUF and RU/FRU. In the C/OX case, FU and RUF are the same, and RU and FRU are opposite to each other. The same goes for the O/CX case, but vice versa. In the OppX case, both FU/RUF and RU/FRU are opposite. This looks like a Z-permutation. Note that all of these cases can be seen as A/A cases at first, but whenever you have an A/A case, you should always look if it isn't the other one.

[[Category:Cubing abbreviations and acronyms]]

OLL

2009-08-17T06:58:35Z

Maarten95: /* OLL 35 */

__NOTOC__
OLL is the [[Orientation]] of the [[Last Layer]], and is the first step in solving the last layer in many speedsolving methods, such as the [[Fridrich Method]].

Parentheses in an algorithm signify the triggers of the algorithm. For example, [(R U R') (L' U L)] shows two triggers in the algorithm, even though it is the same as [R U R' L' U L].

The areas shaded in gray represent the oriented pieces on the top layer. You can tell if a piece is oriented by looking at the top color of the piece in relation to the top center of the cube. If the piece is oriented, the two colors will be the same.

The bars sticking off to the side of an unshaded piece represent where the [[sticker]] that needs to be on top is.

==All edges flipped correctly==
This subgroup, '''OCLL''' is used in methods which have oriented the [[LL]] edges earlier in the solve, such as [[ZZ]] or [[VH]]
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|
=== OLL 21 ===
[[Image:o21.gif]]

* R U R' U R U' R' U R U2 R'
* y R U2 R' U' R U R' U' R U' R'
* y F (R U R' U') (R U R' U') (R U R' U') F'

=== OLL 22 ===
[[Image:o22.gif]]

* R U2 R2' U' R2 U' R2' U2 R
* f (R U R' U') f' F (R U R' U') F'
* y2 L' U2 L2 U L2 U L2 U2 L'
* R U2 R2 U' R' U R U' R U' R' y M' U2 M
* R' U L U' R U' L' U' L U' L'
* y2 L U' R' U L' U R U R' U R
* y2 L' U R U' L U' R' U' R U' R'
* R U' L' U R' U L U L' U L

=== OLL 23 ===
[[Image:o23.gif]]

* R2 D' R U2 R' D R U2 R
* R' U2 R F U' R' U' R U F'
* l2 U' R D2 R' U R D2 R
* l2' U' z' U R2 U' L U R2 z' L
* y' R U R' U' (R U' R' U2)(R U' R' U2) R U R'
* y2 R' F2 R U2 R U2 R' F2 R U2 R'
* y2 R2 D R' U2 R D' R' U2 R'
* (R' U' R U) R' U2 R2 U (R' U R U2 R)

=== OLL 24 ===
[[Image:o24.gif]]

* r U R' U' L' U R U' x'
* r U R' U' r' F R F'
* r U R' U' L' U R U'
* y' R U R2' U' R2 U' R2' U2' R U' R U' R'
* y' R U' R' (U2 R U R') (U2 R U R') (U R U' R')
* y2 R' F' r U R U' r' F
* y2 l' U' L U R U' r' F

||

=== OLL 25 ===
[[Image:o25.gif]]

* y2 R' F R B' R' F' R B
* y' F' r U R' U' r' F R
* y' x U R' U' L U R U' r'
* y R' F' L' F R F' L F
* y R' U' (R U R' F') (R U R' U') (R' F R2)
* y2 R U2' R D R' U2 R D' R2'
* y2 F R' F' r U R U' r'
* y2 l' U R D' R' U' R D x'
* y2 x' L' U' R' U L U' R U
* x' D R U R' D' R U' l'
* x' U L' U' R U L U' l'
* l' U' L' U R U' L U x'
* U r U R U' L' U R' U' x'
* R U2 R' U' R U R' U' R U R' U' R U' R'
* R U R' U R U' R' U R U' R' U R U2 R'

=== OLL 26 ===
[[Image:o26.gif]]

* y2 R' U' R U' R' U2 R
* y' R U2 R' U' R U' R'
* L U2 L' U' L U' L'
* L' U' L U' L' U2 L
* L' U R U' L U R'

=== OLL 27 ===
[[Image:o27.gif]]

* R U R' U R U2 R'
* y' R' U2 R U R' U R
* y L' U2 L U L' UL
* y2 L U L' U L U2 L'
* R U' L' U R' U' L

|}

==No edges flipped correctly==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 1 ===
[[Image:o1.gif]]

* (R U2) (R2' F R F' U2') (R' F R F')
* R U B' R B R2 U' R' F R F'

=== OLL 2 ===
[[Image:o2.gif]]

* F (R U R' U') F' f (R U R' U') f'

=== OLL 3 ===
[[Image:o3.gif]]

* y f (R U R' U') f' U' F (R U R' U') F'
* y2 r' R2 U R' U r U2 r' U R' r

=== OLL 4 ===
[[Image:o4.gif]]

* f (R U R' U') f' U F (R U R' U') F'
* R' U2 x R' U R U' y R' U' R' U R' F
* y r' R U' r U2 r' U' R U' R2' r

||

=== OLL 17 ===
[[Image:o17.gif]]

* R U R' U R' F R F' U2 R' F R F'

=== OLL 18 ===
[[Image:o18.gif]]

* y' r U R' U R U2 r2' U' R U' R' U2 r
* y2 F R U R' d R' U2 R' F R F'
* R U2 R2 F R F' U2 M' U R U' r'

=== OLL 19 ===
[[Image:o19.gif]]

* r' U2 R U R' U r2 U2' R' U' R U' r'
* R' U2 F R U R' U' y' R2 U2 R B
* r' R U R U R' U' r R2' F R F'
* M U R U R' U' r R2' F R F'

=== OLL 20 ===
[[Image:o20.gif]]

* r' R U R U R' U' r2 R2' U R U' r'
* M U R U R' U' M2 U R U' r'
* M' U2 M' U2 M' U M U2 M U2 M
* M' U2 M U2 M' U M U2 M' U2 M
* M d r2 U M' U2 M U r2 S'
* M' U M' U M' U M' U M U M U M U M U
* (r U R' U') M2 (U R U' R') U' M'
|}

=="P" shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 31 ===
[[Image:o31.gif]]

* L' d' R d L U' L' B' L
* S' L' U' L U L F' L' f
* y x U R' U' l U R U R' U' R U' R'
* y2 R' U' F U R U' R' F' R
* L' U' B U L U' L' B' L

=== OLL 32 ===
[[Image:o32.gif]]

* R d L' d' R' U R B R'
* S R U R' U' R' F R f'
* y x' U' R U l' U' R' U' R U R' U R
* R U B' U' R' U R B R'
* y2 F U R U' F' r U R' U' r'

||

=== OLL 43 ===
[[Image:o43.gif]]

* f' L' U' L U f
* B' U' R' U R B
* y2 F' U' L' U L F
* U R U R' F' L' U' L F
* y2 R' U' F R' F' R U R

=== OLL 44 ===
[[Image:o44.gif]]

* f R U R' U' f'
* y2 F U R U' R' F'
* y R U y' L U' L' B'

|}

=="W" shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 36 ===
[[Image:o36.gif]]

* R' U' R U' R' U R U R B' R' B
* y2 (L' U' L U') (L' U L U) (L F' L' F)
* (R U R' U') y (L' U2' L U) y' (R U R')
||

=== OLL 38 ===
[[Image:o38.gif]]

* L U L' U L U' L' U' L' B L B'
* y2 R U R' U R U' R' U' R' F R F'
* (L' U' L U) y' (R U2 R' U') y (L' U' L)
|}

=="L" shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 53 ===
[[Image:o53.gif]]

* l' U' L U' L' U L U' L' U2 l
* y2 r' U' R U' R' U R U' R' U2 r
* y' r' U2 R U R' U' R U R' U r

=== OLL 54 ===
[[Image:o54.gif]]

* r U R' U R U' R' U R U2 r'
* y' r U2 R' U' R U R' U' R U' r'

=== OLL 50 ===
[[Image:o50.gif]]

* y2 R' F R2 B' R2 F' R2 B R'
* r' U r2 U' r2' U' r2 U r'
* R B' R B R2' U2 F R' F' R
* y2 l' U l2 U' l2 U' l2 U l'
* r' U2 R2' U R2 U rR U2 R'
* y' [R U2 R' U' R U' R'] [F R U R' U' F']
* (y x') U' r U2 L' U2 r' U2 L U' (x)

||

=== OLL 47 ===
[[Image:o47.gif]]

* F' L' U' L U L' U' L U F
* R' U' x R' U R U' R' U R U' x' U R
* b' U' R' U R U' R' U R b

=== OLL 48 ===
[[Image:o48.gif]]

* F R U R' U' R U R' U' F'
* y2 f U R U' R' U R U' R' f'

=== OLL 49 ===
[[Image:o49.gif]]

* R B' R2 F R2 B R2 F' R
* l U' l2' U l2 U l2' U' l
* y2 r U' r2 U r2 U r2 U' r
* y2 R' F R' F' R2 d2 y' R' F R F'
* y2 r U2 R2' U' R2 U' r'R' U2 R
* (y' x') U l' U2 R U2 l U2 R' U (x)

|}

=="C" shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 34 ===
[[Image:o34.gif]]

* R U R' U' x D' R' U R E'
* R U R' d' l' U' L U r' R
* y2 F R U R' U' R' F' r U R U' r'
||

=== OLL 46 ===
[[Image:o46.gif]]

* R' U' R' F R F' U R
* R' U' l' U l F' U R
* R U l U' R' U F' l'
* y2 L F U' R U R' F' L'
* R U R'2 U' R' F R U R U' F

|}

=="T" shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 33 ===
[[Image:o33.gif]]

* R U R' U' R' F R F'
* R' U' R U l U' R' U (x)

||

=== OLL 45 ===
[[Image:o45.gif]]

* F R U R' U' F'

|}

=="I" shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 55 ===
[[Image:o55.gif]]

* R U2 R2 U' R U' R' U2 F R F'
** A 4x4x4 special: Note: Rra = (R + r) + (L + l)
::(y) Rr U2 Rra' U2 Rr U2 Rr' U2 Rra U2 Rr'
* y R' F R U R' F R U' R' F' R U M' U' M
* L F' L' U' L F' L' U L F L' U' M' U M
* (L F' L' U' L F' L' U L F L' U' L)(R' F R) L'
* R d' R2 D R' U2 R D' R2 d R'

=== OLL 56 ===
[[Image:o56.gif]]

* R B R' U L U' L' U L U' L' R B' R'
* r' U' r U' R' U R U' R' U R r' U r
* F R U R' U' R F' r U R' U' r'

||

=== OLL 51 ===
[[Image:o51.gif]]

* F U R U' R' U R U' R' F'
* y2 f R U R' U' R U R' U' f'

=== OLL 52 ===
[[Image:o52.gif]]

* R' U' R U' R' d R' U R B
* R U R' U R d' R U' R' F'
* R U R' U R U2 R' (Sune) U (F U R U' R' F')

|}

==Square shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 5 ===
[[Image:o5.gif]]

* (r' U2) (R U R' U r)
* y2 l' U2 L U L' U l'

||

=== OLL 6 ===
[[Image:o6.gif]]

* y2 (r U2) (R' U' R U') r'
* l U2 L' U' L U' l'
|}

==Big lightning bolt shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 39 ===
[[Image:o39.gif]]

* L F' L' U' L U F U' L'
* y2 f' L F L' U' L' U L S
* y2 R B' R' U' R U B U' R'

||

=== OLL 40 ===
[[Image:o40.gif]]

* R' F R U R' U' F' U R
* y2 f R' F' R U R U' R' S'
* y2 L' B L U L' U' B' U L

|}

==Small lightning bolt shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 7 ===
[[Image:o7.gif]]

* (r U R' U) (R U2 r')
* L' U2 L U2 L F' L' F

=== OLL 8 ===
[[Image:o8.gif]]

* y2 r' U' R U' R' U2 r
* R U2 R' U2 R' F R F'

||

=== OLL 11 ===
[[Image:o11.gif]]

* r' R2 U R' U R U2 R' U r R'
* y2 r U R' U R' F R F' R U2 r'
* y F' L' U' L U F' Y F R U R' U' F'

=== OLL 12 ===
[[Image:o12.gif]]

* F R U R' U' F' y F R U R' U' F'
* y F R U R2 F R y' R2 U R U2 R'
* y' r R2 U' R U' R' U2 R U' R r'

|}

==Fish shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 9 ===
[[Image:o9.gif]]

* y' R' U' R y' x' R U' R' F R U R' x
* y' R U R' U' R' F R2 U R' U' F'

=== OLL 10 ===
[[Image:o10.gif]]

* y' R U R' y R' F R U' R' F' R

* y' R' U' R U R B' R2 U' R U B
||

=== OLL 35 ===
[[Image:o35.gif]]

* R U2 R2' F R F' R U2 R'
* y' R' U2 (R Lw) U' R' U Lw' U2 R

=== OLL 37 ===
[[Image:o37.gif]]

* x' U' R U l' U' R' U R
* l U' R' U y' R U R' U' z'
* y F R U' R' U' R U R' F'
* y R' F R F' U' F' U F
* y F R' F' R U R U' R'
* R B' R' B U B U' B'

|}

==Knight move shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 13 ===
[[Image:o13.gif]]

* F U R U' R2 F' R U R U' R'
* F U R U2 R' U' R U R' F'
* y2 x' R U' R' F' R U R' x y R' U R
* y2 f R U R2 U' R' U R U' f'
* r U' r' U' r U r' y' R' U R

=== OLL 14 ===
[[Image:o14.gif]]

* R' F R U R' F' R y' R U' R'
* y' R' U' y' R' U R2 B R' U' R' U R
* y2 B' U' R' U R2 B R' U' R' U R
||

=== OLL 15 ===
[[Image:o15.gif]]

* y2 R' F' R L' U' L U R' F R
* r' U' r R' U' R U r' U r

=== OLL 16 ===
[[Image:o16.gif]]

* y2 r U r' R U R' U' r U' r'
* y2 r U M U R' U' r U' r'

|}

==Awkward shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 29 ===
[[Image:o29.gif]]

* y2 R' F R F' R U2 R' d' L' U' L
* y2 R2' U' R F R' U R2' U' R' F' R
* y (R U R' U') (R U' R' F') U' (F R U R')
* y R' U2 R2 U R' U' R' U2 F R F'
* M U (R U R' U') (R' F R F') M'

=== OLL 30 ===
[[Image:o30.gif]]

* l U' R' U l' U2 d L U L'
* f R U R2 U' R' U R2 U' R' f'
* y2 F U R U' x' U R' D' R U' R'
* R2' U R' B' R U' R2' U R B R'
* M U' (L' U' L U) (L F' L' F) M'

||

=== OLL 41 ===
[[Image:o41.gif]]

* R U' R' U2 R U y R U' R' U' F'
* y R U2' R' U' R U' R2 (y) L' U' L U F
* y2 F U R U' R' F' R' U2 R U R' U R
* y2 R U R' U R U2 R' F R U R' U' F'
* y2 R2 L z' l' U' R d L U' L l'

=== OLL 42 ===
[[Image:o42.gif]]

* L' U L U2 L' U' y' L' U L U F
* y R' U2 R U R' U R2 y R U R' U' F'
* y R' F R F' R' F R F' R U R' U' R U R'
* y2 L2 R' z r U L' d' R' U R' r

|}

==All Corners Oriented==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 28 ===
[[Image:o28.gif]]

* r U R' U' r' R U R U' R'
* F R U R' U' F' U2 F R U R' U' F'
* y2 M' U M U2 M' U M
* M U M' U2 M U M'

||

=== OLL 57 ===
[[Image:o57.gif]]

* R U R' U' r R' U R U' r'
* (x') M' U' R U M U' R' U (x)
* M U M U M U2 M' U M' U M' U2
* y M' U M' U M' U M' U M' U' M' U' M' U' M' U'

|}

[[Category:3x3x3 methods]]
[[Category:Cubing abbreviations and acronyms]]
[[Category:Algorithms]]

OLL

2009-08-17T06:55:27Z

Maarten95: /* OLL 33 */

__NOTOC__
OLL is the [[Orientation]] of the [[Last Layer]], and is the first step in solving the last layer in many speedsolving methods, such as the [[Fridrich Method]].

Parentheses in an algorithm signify the triggers of the algorithm. For example, [(R U R') (L' U L)] shows two triggers in the algorithm, even though it is the same as [R U R' L' U L].

The areas shaded in gray represent the oriented pieces on the top layer. You can tell if a piece is oriented by looking at the top color of the piece in relation to the top center of the cube. If the piece is oriented, the two colors will be the same.

The bars sticking off to the side of an unshaded piece represent where the [[sticker]] that needs to be on top is.

==All edges flipped correctly==
This subgroup, '''OCLL''' is used in methods which have oriented the [[LL]] edges earlier in the solve, such as [[ZZ]] or [[VH]]
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|
=== OLL 21 ===
[[Image:o21.gif]]

* R U R' U R U' R' U R U2 R'
* y R U2 R' U' R U R' U' R U' R'
* y F (R U R' U') (R U R' U') (R U R' U') F'

=== OLL 22 ===
[[Image:o22.gif]]

* R U2 R2' U' R2 U' R2' U2 R
* f (R U R' U') f' F (R U R' U') F'
* y2 L' U2 L2 U L2 U L2 U2 L'
* R U2 R2 U' R' U R U' R U' R' y M' U2 M
* R' U L U' R U' L' U' L U' L'
* y2 L U' R' U L' U R U R' U R
* y2 L' U R U' L U' R' U' R U' R'
* R U' L' U R' U L U L' U L

=== OLL 23 ===
[[Image:o23.gif]]

* R2 D' R U2 R' D R U2 R
* R' U2 R F U' R' U' R U F'
* l2 U' R D2 R' U R D2 R
* l2' U' z' U R2 U' L U R2 z' L
* y' R U R' U' (R U' R' U2)(R U' R' U2) R U R'
* y2 R' F2 R U2 R U2 R' F2 R U2 R'
* y2 R2 D R' U2 R D' R' U2 R'
* (R' U' R U) R' U2 R2 U (R' U R U2 R)

=== OLL 24 ===
[[Image:o24.gif]]

* r U R' U' L' U R U' x'
* r U R' U' r' F R F'
* r U R' U' L' U R U'
* y' R U R2' U' R2 U' R2' U2' R U' R U' R'
* y' R U' R' (U2 R U R') (U2 R U R') (U R U' R')
* y2 R' F' r U R U' r' F
* y2 l' U' L U R U' r' F

||

=== OLL 25 ===
[[Image:o25.gif]]

* y2 R' F R B' R' F' R B
* y' F' r U R' U' r' F R
* y' x U R' U' L U R U' r'
* y R' F' L' F R F' L F
* y R' U' (R U R' F') (R U R' U') (R' F R2)
* y2 R U2' R D R' U2 R D' R2'
* y2 F R' F' r U R U' r'
* y2 l' U R D' R' U' R D x'
* y2 x' L' U' R' U L U' R U
* x' D R U R' D' R U' l'
* x' U L' U' R U L U' l'
* l' U' L' U R U' L U x'
* U r U R U' L' U R' U' x'
* R U2 R' U' R U R' U' R U R' U' R U' R'
* R U R' U R U' R' U R U' R' U R U2 R'

=== OLL 26 ===
[[Image:o26.gif]]

* y2 R' U' R U' R' U2 R
* y' R U2 R' U' R U' R'
* L U2 L' U' L U' L'
* L' U' L U' L' U2 L
* L' U R U' L U R'

=== OLL 27 ===
[[Image:o27.gif]]

* R U R' U R U2 R'
* y' R' U2 R U R' U R
* y L' U2 L U L' UL
* y2 L U L' U L U2 L'
* R U' L' U R' U' L

|}

==No edges flipped correctly==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 1 ===
[[Image:o1.gif]]

* (R U2) (R2' F R F' U2') (R' F R F')
* R U B' R B R2 U' R' F R F'

=== OLL 2 ===
[[Image:o2.gif]]

* F (R U R' U') F' f (R U R' U') f'

=== OLL 3 ===
[[Image:o3.gif]]

* y f (R U R' U') f' U' F (R U R' U') F'
* y2 r' R2 U R' U r U2 r' U R' r

=== OLL 4 ===
[[Image:o4.gif]]

* f (R U R' U') f' U F (R U R' U') F'
* R' U2 x R' U R U' y R' U' R' U R' F
* y r' R U' r U2 r' U' R U' R2' r

||

=== OLL 17 ===
[[Image:o17.gif]]

* R U R' U R' F R F' U2 R' F R F'

=== OLL 18 ===
[[Image:o18.gif]]

* y' r U R' U R U2 r2' U' R U' R' U2 r
* y2 F R U R' d R' U2 R' F R F'
* R U2 R2 F R F' U2 M' U R U' r'

=== OLL 19 ===
[[Image:o19.gif]]

* r' U2 R U R' U r2 U2' R' U' R U' r'
* R' U2 F R U R' U' y' R2 U2 R B
* r' R U R U R' U' r R2' F R F'
* M U R U R' U' r R2' F R F'

=== OLL 20 ===
[[Image:o20.gif]]

* r' R U R U R' U' r2 R2' U R U' r'
* M U R U R' U' M2 U R U' r'
* M' U2 M' U2 M' U M U2 M U2 M
* M' U2 M U2 M' U M U2 M' U2 M
* M d r2 U M' U2 M U r2 S'
* M' U M' U M' U M' U M U M U M U M U
* (r U R' U') M2 (U R U' R') U' M'
|}

=="P" shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 31 ===
[[Image:o31.gif]]

* L' d' R d L U' L' B' L
* S' L' U' L U L F' L' f
* y x U R' U' l U R U R' U' R U' R'
* y2 R' U' F U R U' R' F' R
* L' U' B U L U' L' B' L

=== OLL 32 ===
[[Image:o32.gif]]

* R d L' d' R' U R B R'
* S R U R' U' R' F R f'
* y x' U' R U l' U' R' U' R U R' U R
* R U B' U' R' U R B R'
* y2 F U R U' F' r U R' U' r'

||

=== OLL 43 ===
[[Image:o43.gif]]

* f' L' U' L U f
* B' U' R' U R B
* y2 F' U' L' U L F
* U R U R' F' L' U' L F
* y2 R' U' F R' F' R U R

=== OLL 44 ===
[[Image:o44.gif]]

* f R U R' U' f'
* y2 F U R U' R' F'
* y R U y' L U' L' B'

|}

=="W" shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 36 ===
[[Image:o36.gif]]

* R' U' R U' R' U R U R B' R' B
* y2 (L' U' L U') (L' U L U) (L F' L' F)
* (R U R' U') y (L' U2' L U) y' (R U R')
||

=== OLL 38 ===
[[Image:o38.gif]]

* L U L' U L U' L' U' L' B L B'
* y2 R U R' U R U' R' U' R' F R F'
* (L' U' L U) y' (R U2 R' U') y (L' U' L)
|}

=="L" shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 53 ===
[[Image:o53.gif]]

* l' U' L U' L' U L U' L' U2 l
* y2 r' U' R U' R' U R U' R' U2 r
* y' r' U2 R U R' U' R U R' U r

=== OLL 54 ===
[[Image:o54.gif]]

* r U R' U R U' R' U R U2 r'
* y' r U2 R' U' R U R' U' R U' r'

=== OLL 50 ===
[[Image:o50.gif]]

* y2 R' F R2 B' R2 F' R2 B R'
* r' U r2 U' r2' U' r2 U r'
* R B' R B R2' U2 F R' F' R
* y2 l' U l2 U' l2 U' l2 U l'
* r' U2 R2' U R2 U rR U2 R'
* y' [R U2 R' U' R U' R'] [F R U R' U' F']
* (y x') U' r U2 L' U2 r' U2 L U' (x)

||

=== OLL 47 ===
[[Image:o47.gif]]

* F' L' U' L U L' U' L U F
* R' U' x R' U R U' R' U R U' x' U R
* b' U' R' U R U' R' U R b

=== OLL 48 ===
[[Image:o48.gif]]

* F R U R' U' R U R' U' F'
* y2 f U R U' R' U R U' R' f'

=== OLL 49 ===
[[Image:o49.gif]]

* R B' R2 F R2 B R2 F' R
* l U' l2' U l2 U l2' U' l
* y2 r U' r2 U r2 U r2 U' r
* y2 R' F R' F' R2 d2 y' R' F R F'
* y2 r U2 R2' U' R2 U' r'R' U2 R
* (y' x') U l' U2 R U2 l U2 R' U (x)

|}

=="C" shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 34 ===
[[Image:o34.gif]]

* R U R' U' x D' R' U R E'
* R U R' d' l' U' L U r' R
* y2 F R U R' U' R' F' r U R U' r'
||

=== OLL 46 ===
[[Image:o46.gif]]

* R' U' R' F R F' U R
* R' U' l' U l F' U R
* R U l U' R' U F' l'
* y2 L F U' R U R' F' L'
* R U R'2 U' R' F R U R U' F

|}

=="T" shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 33 ===
[[Image:o33.gif]]

* R U R' U' R' F R F'
* R' U' R U l U' R' U (x)

||

=== OLL 45 ===
[[Image:o45.gif]]

* F R U R' U' F'

|}

=="I" shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 55 ===
[[Image:o55.gif]]

* R U2 R2 U' R U' R' U2 F R F'
** A 4x4x4 special: Note: Rra = (R + r) + (L + l)
::(y) Rr U2 Rra' U2 Rr U2 Rr' U2 Rra U2 Rr'
* y R' F R U R' F R U' R' F' R U M' U' M
* L F' L' U' L F' L' U L F L' U' M' U M
* (L F' L' U' L F' L' U L F L' U' L)(R' F R) L'
* R d' R2 D R' U2 R D' R2 d R'

=== OLL 56 ===
[[Image:o56.gif]]

* R B R' U L U' L' U L U' L' R B' R'
* r' U' r U' R' U R U' R' U R r' U r
* F R U R' U' R F' r U R' U' r'

||

=== OLL 51 ===
[[Image:o51.gif]]

* F U R U' R' U R U' R' F'
* y2 f R U R' U' R U R' U' f'

=== OLL 52 ===
[[Image:o52.gif]]

* R' U' R U' R' d R' U R B
* R U R' U R d' R U' R' F'
* R U R' U R U2 R' (Sune) U (F U R U' R' F')

|}

==Square shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 5 ===
[[Image:o5.gif]]

* (r' U2) (R U R' U r)
* y2 l' U2 L U L' U l'

||

=== OLL 6 ===
[[Image:o6.gif]]

* y2 (r U2) (R' U' R U') r'
* l U2 L' U' L U' l'
|}

==Big lightning bolt shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 39 ===
[[Image:o39.gif]]

* L F' L' U' L U F U' L'
* y2 f' L F L' U' L' U L S
* y2 R B' R' U' R U B U' R'

||

=== OLL 40 ===
[[Image:o40.gif]]

* R' F R U R' U' F' U R
* y2 f R' F' R U R U' R' S'
* y2 L' B L U L' U' B' U L

|}

==Small lightning bolt shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 7 ===
[[Image:o7.gif]]

* (r U R' U) (R U2 r')
* L' U2 L U2 L F' L' F

=== OLL 8 ===
[[Image:o8.gif]]

* y2 r' U' R U' R' U2 r
* R U2 R' U2 R' F R F'

||

=== OLL 11 ===
[[Image:o11.gif]]

* r' R2 U R' U R U2 R' U r R'
* y2 r U R' U R' F R F' R U2 r'
* y F' L' U' L U F' Y F R U R' U' F'

=== OLL 12 ===
[[Image:o12.gif]]

* F R U R' U' F' y F R U R' U' F'
* y F R U R2 F R y' R2 U R U2 R'
* y' r R2 U' R U' R' U2 R U' R r'

|}

==Fish shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 9 ===
[[Image:o9.gif]]

* y' R' U' R y' x' R U' R' F R U R' x
* y' R U R' U' R' F R2 U R' U' F'

=== OLL 10 ===
[[Image:o10.gif]]

* y' R U R' y R' F R U' R' F' R

* y' R' U' R U R B' R2 U' R U B
||

=== OLL 35 ===
[[Image:o35.gif]]

* R U2 R2' F R F' R U2 R'

=== OLL 37 ===
[[Image:o37.gif]]

* x' U' R U l' U' R' U R
* l U' R' U y' R U R' U' z'
* y F R U' R' U' R U R' F'
* y R' F R F' U' F' U F
* y F R' F' R U R U' R'
* R B' R' B U B U' B'

|}

==Knight move shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 13 ===
[[Image:o13.gif]]

* F U R U' R2 F' R U R U' R'
* F U R U2 R' U' R U R' F'
* y2 x' R U' R' F' R U R' x y R' U R
* y2 f R U R2 U' R' U R U' f'
* r U' r' U' r U r' y' R' U R

=== OLL 14 ===
[[Image:o14.gif]]

* R' F R U R' F' R y' R U' R'
* y' R' U' y' R' U R2 B R' U' R' U R
* y2 B' U' R' U R2 B R' U' R' U R
||

=== OLL 15 ===
[[Image:o15.gif]]

* y2 R' F' R L' U' L U R' F R
* r' U' r R' U' R U r' U r

=== OLL 16 ===
[[Image:o16.gif]]

* y2 r U r' R U R' U' r U' r'
* y2 r U M U R' U' r U' r'

|}

==Awkward shapes==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 29 ===
[[Image:o29.gif]]

* y2 R' F R F' R U2 R' d' L' U' L
* y2 R2' U' R F R' U R2' U' R' F' R
* y (R U R' U') (R U' R' F') U' (F R U R')
* y R' U2 R2 U R' U' R' U2 F R F'
* M U (R U R' U') (R' F R F') M'

=== OLL 30 ===
[[Image:o30.gif]]

* l U' R' U l' U2 d L U L'
* f R U R2 U' R' U R2 U' R' f'
* y2 F U R U' x' U R' D' R U' R'
* R2' U R' B' R U' R2' U R B R'
* M U' (L' U' L U) (L F' L' F) M'

||

=== OLL 41 ===
[[Image:o41.gif]]

* R U' R' U2 R U y R U' R' U' F'
* y R U2' R' U' R U' R2 (y) L' U' L U F
* y2 F U R U' R' F' R' U2 R U R' U R
* y2 R U R' U R U2 R' F R U R' U' F'
* y2 R2 L z' l' U' R d L U' L l'

=== OLL 42 ===
[[Image:o42.gif]]

* L' U L U2 L' U' y' L' U L U F
* y R' U2 R U R' U R2 y R U R' U' F'
* y R' F R F' R' F R F' R U R' U' R U R'
* y2 L2 R' z r U L' d' R' U R' r

|}

==All Corners Oriented==
{|border="0" width="100%" valign="top"
|-valign="top"
|width="50%"|
|width="50%"|
|-valign="top"
|

=== OLL 28 ===
[[Image:o28.gif]]

* r U R' U' r' R U R U' R'
* F R U R' U' F' U2 F R U R' U' F'
* y2 M' U M U2 M' U M
* M U M' U2 M U M'

||

=== OLL 57 ===
[[Image:o57.gif]]

* R U R' U' r R' U R U' r'
* (x') M' U' R U M U' R' U (x)
* M U M U M U2 M' U M' U M' U2
* y M' U M' U M' U M' U M' U' M' U' M' U' M' U'

|}

[[Category:3x3x3 methods]]
[[Category:Cubing abbreviations and acronyms]]
[[Category:Algorithms]]

ZBLL

2009-08-14T07:10:39Z

Maarten95:

'''ZBLL''' (short for ''[[Zbigniew Zborowski|Zborowski]]-[[Ron van Bruchem|Bruchem]] Last Layer'') is a step of a method which involves solving the entire [[last layer]] in one step, assuming that the [[edge]]s are already oriented. This is part of the [[ZB method]], but it can be useful for any other method which leaves the edges of the last layer oriented after F2L is solved (such as the [[Petrus method]]).

ZBLL indeed sounds like a very useful step to learn, but the main reason that it is not in wide use is that it involves a massive 177 algorithms (counting inverses and mirrors are the same), or a total of 493 cases. Only a handful of people have ever learned this step in its entirety. If you wish to learn it, it is useful to start by learning either [[OCLL]]/[[PLL]] or [[COLL]]/[[EPLL]], so that you will always be able to finish the cube relatively quickly even if you do not yet know the ZBLL case.

The ZBLL cases are divided into 7 sets: T, U, L, Pi, Sune, Anti-sune, H, and the Pll cases, in which all pieces are oriented. The sets are then divided further into 40 subsets. They are recognized by their [[COLL]] case as well as a corresponding edge cycle. Every subset contains 12 cases, which are all different edge cycles possible with the COLL case of that set. Many people recognize ZBLL by looking at the UFR corner, and its neighboring stickers. Whether the stickers are adjacent, or opposite allows for a quick recognition. However, this method only works for the T, U and L subsets of ZBLL, because in the other cases the UFR corner is not correctly oriented. Another way to recognize is through blocks of colour or simply the edge cycle.

For the T, U and L cases (there are 3*6*12=216 algorithms in this set) recognition goes as follows:

1. Recognize the orientation case.

2. Recognize the [[COLL]] case.

3. Recognize the edge cycle by looking at the UFR corner and the edge stickers around it.

4. Apply the corresponding algorithm.

Step 3 may look a little complicated, but it's actually not too bad. In total there's 12 cases, but those are recognized by 2 minor sub-cases, of which there are 3:

C: If the FU sticker is the same as the FRU sticker, and if the RU sticker is the same as the RUF sticker.

A: If the FU sticker is an adjacent color to the FRU sticker, and if the RU sticker is an adjacent color to the RUF sticker.

O: If FU and FRU are opposite, and if RU and RUF are opposite.

A case is recognized by the combination of those. First comes the FU/FRU relation, then the RU/RUF relation, divided by a slash. That means there are 9 possibilities with these cases: C/C, C/A, C/O, A/C, A/A, A/O, O/C, O/A, O/O. However, there are 12 cases. That's because the A case can mean 2 stickers. That's why the last 3 cases are known as C/OX, O/CX and OppX. This means that you don't look for the relation between FU/FRU and RU/RUF, but between FU/RUF and RU/FRU. In the C/OX case, FU and RUF are the same, and RU and FRU are opposite to each other. The same goes for the O/CX case, but vice versa. In the OppX case, both FU/RUF and RU/FRU are opposite. This looks like a Z-permutation. Note that all of these cases can be seen as A/A cases at first, but whenever you have an A/A case, you should always look if it isn't the other one.

[[Category:Cubing abbreviations and acronyms]]

ZBLL

2009-08-14T06:33:41Z

Maarten95:

'''ZBLL''' (short for ''[[Zbigniew Zborowski|Zborowski]]-[[Ron van Bruchem|Bruchem]] Last Layer'') is a step of a method which involves solving the entire [[last layer]] in one step, assuming that the [[edge]]s are already oriented. This is part of the [[ZB method]], but it can be useful for any other method which leaves the edges of the last layer oriented after F2L is solved (such as the [[Petrus method]]).

ZBLL indeed sounds like a very useful step to learn, but the main reason that it is not in wide use is that it involves a massive 177 algorithms (counting inverses and mirrors are the same), or a total of 493 cases. Only a handful of people have ever learned this step in its entirety. If you wish to learn it, it is useful to start by learning either [[OCLL]]/[[PLL]] or [[COLL]]/[[EPLL]], so that you will always be able to finish the cube relatively quickly even if you do not yet know the ZBLL case.

The ZBLL cases are divided into 7 sets: T, U, L, Pi, Sune, Anti-sune, H, and the Pll cases, in which all pieces are oriented. The sets are then divided further into 40 subsets. They are recognized by their [[COLL]] case as well as a corresponding edge cycle. Every subset contains 12 cases, which are all different edge cycles possible with the COLL case of that set. Many people recognize ZBLL by looking at the UFR corner, and its neighboring stickers. Whether the stickers are adjacent, or opposite allows for a quick recognition. However, this method only works for the T, U and L subsets of ZBLL, because in the other cases the UFR corner is not correctly oriented. Another way to recognize is through blocks of colour or simply the edge cycle.

For the T, U and L cases (there are 3*6*12=216 algorithms in this set) recognition goes as follows:

1. Recognize the orientation case.
2. Recognize the [[COLL]] case.
3. Recognize the edge cycle by looking at the UFR corner and the edge stickers around it.
4. Apply the corresponding algorithm.

Step 3 may look a little complicated, but it's actually not too bad. In total there's 12 cases, but those are recognized by 2 minor sub-cases, of which there are 3:

C: If the FU sticker is the same as the FRU sticker, and if the RU sticker is the same as the RUF sticker.
A: If the FU sticker is an adjacent color to the FRU sticker, and if the RU sticker is an adjacent color to the RUF sticker.
O: If FU and FRU are opposite, and if RU and RUF are opposite.

A case is recognized by the combination of those. First comes the FU/FRU relation, then the RU/RUF relation, divided by a slash. That means there are 9 possibilities with these cases: C/C, C/A, C/O, A/C, A/A, A/O, O/C, O/A, O/O. However, there are 12 cases. That's because the A case can mean 2 stickers. That's why the last 3 cases are known as C/OX, O/CX and OppX. This means that you don't look for the relation between FU/FRU and RU/RUF, but between FU/RUF and RU/FRU. In the C/OX case, FU and RUF are the same, and RU and FRU are opposite to each other. The same goes for the O/CX case, but vice versa. In the OppX case, both FU/RUF and RU/FRU are opposite. This looks like a Z-permutation. Note that all of these cases can be seen as A/A cases at first, but whenever you have an A/A case, you should always look if it isn't the other one.

[[Category:Cubing abbreviations and acronyms]]