56-8
Double 3x1 bars
Set up
R U' F R2 U R' U' R2 F' U2 R2 F R F'
Algorithm
?FR'F'R2U2'FR2'URU'R2F'UR'
FR'F'R2U2'FRR2'ULRU'right → overhandR2F'RULR'
Introduction to 1LLL 56
Learning 1LLL might sound ridiculous, but 1LLL 56 is one of the very few subsets actually worth learning. Once you recognize OLL 56, identifying the specific case just requires looking at the top face, and, with practice, can be done almost instantly.
1LLL 56
Your 1LLL 56 progress
Counts every case you have marked as Learning.
Whole set0/40 learnt
Group A · Two Pairs of Horizontally Matching Corners
Group A0/8 learnt
Class A1: With a 3x1 bar3 cases
Class A10/3 learnt
56-3
Outstanding edge?the edge which is not part of the 3x1 bar needs to go clockwise
How to recognize
In this example, imagine the Red edge needs to go clockwise because in the standard color scheme, Red follows Green (i.e. color of adjacent corners) in the clockwise direction when Yellow is on top. Recognition could be difficult at first but your brain will get used to it with practice.
Set up
R U' R2 Rw U' R U R' U R Rw' R U R' U'
Algorithm
?(U)RU'R'M'U'RU'R'UMRUR'
(U)RU'R'M'LU'RU'R'UMLRUR'
56-4
Outstanding edge?the edge which is not part of the 3x1 bar needs to go counterclockwise
How to recognize
In this example, imagine the Red edge needs to go counterclockwise because in the standard color scheme, Red follows Blue (i.e. color of adjacent corners) in the counterclockwise direction when Yellow is on top. Recognition could be difficult at first but your brain will get used to it with practice.
Set up
R U' R' U' F' U R U R2' U' R' F R U R U2
Algorithm
?(U)(R'URU)S'(R'UR)SU'R'U'R
(U)R'ULRUS'R'ULRSU'R'U'R
Class A2: With an opposite headlight3 cases
Class A20/3 learnt
56-7
Double opposite headlights
Set up
Rw U2' R' U' M R U R' U' Rw U' Rw'
Algorithm
?RwURw'URU'R'M'URU2'Rw'
RwURw'URRU'R'M'LURU2'Rw'
56-1
Outstanding edge?the edge which is not part of the opposite headlight needs to go clockwise
How to recognize
In this example, imagine the Orange edge needs to go clockwise because in the standard color scheme, Orange follows Blue (i.e. color of adjacent corners) in the clockwise direction when Yellow is on top. Recognition could be difficult at first but your brain will get used to it with practice.
Set up
Rw' U' Rw R' U' R U R' U' R U Rw' U Rw U2
Algorithm
?(U2)Rw'U'RwU'R'URU'R'UMURw
(U2)Rw'U'RwU'R'ULRU'R'ULMRULRw
56-2
Outstanding edge?the edge which is not part of the opposite headlight needs to go counterclockwise
How to recognize
In this example, imagine the Orange edge needs to go counterclockwise because in the standard color scheme, Orange follows Green (i.e. color of adjacent corners) in the counterclockwise direction when Yellow is on top. Recognition could be difficult at first but your brain will get used to it with practice.
Set up
Rw U Rw' R U R' U' R U R' U' Rw U' Rw' U2
Algorithm
?(U2)RwURw'URU'R'URU'R'RwU'Rw'
(U2)RwURw'URRU'R'URU'R'RwU'Rw'
Class A3: Double adjacent headlights2 cases
Class A30/2 learnt
56-6
Edges need to go clockwise
How to recognize
In this example, imagine the Red (Orange) edge needs to go clockwise because in the standard color scheme, Red (Orange) follows Green (Blue) (i.e. color of adjacent corners) in the clockwise direction when Yellow is on top. Recognition could be difficult at first but your brain will get used to it with practice.
Set up
R U2 R' F' U2 F R' U' R2 U' R2 U2 F R F'
Algorithm
?(U)RU2'SU2'RU2'R'U2'R'S'R'
(U)right → overhandRU2'SU2'RU2'R'U2'right → underhandR'S'R'
56-5
Edges need to go counterclockwise
How to recognize
In this example, imagine the Red (Orange) edge needs to go counterclockwise because in the standard color scheme, Red (Orange) follows Blue (Green) (i.e. color of adjacent corners) in the counterclockwise direction when Yellow is on top. Recognition could be difficult at first but your brain will get used to it with practice.
Set up
R' U' Uw' R U2' R U2' R' U' Uw R2' U2' R' U'
Algorithm
?(U)RSRU2'RU2R'U2'S'U2R'
(U)right → overhandRSRU2'RRU2'R'U2S'U2R'
Group B · Two Pairs of Vertically Matching Corners ("Dumbbell Case")
Group B0/8 learnt
Class B1: L/Checkmark6 cases
Class B10/6 learnt
56-15
Double checkmarks
Set up
F R U R' U' F' R' U2 R2 U R2 U R2 U2 R' U
Algorithm
?(U')RU2'R2'U'R2U'R2'U2'RFURU'R'F'
(U')RU2'R2'U'R2U'R2'U2'RFRURRU'R'F'
56-16
Double Ls
Set up
F R U' R' U' R U R' F' U' F R' F' R U2' R U2' R' U'
Algorithm
?(U)RU2'R'U2R'FRF'UFRU'R'URUR'F'
(U)RU2'R'U2R'FRF'URFRRU'R'URUR'F'
56-11
L embracing “clockwise edge”
How to recognize
In this example, the Red edge is considered a “clockwise edge” because in the standard color scheme, Red (color of edge embraced) follows Green (color of L) in the clockwise direction when Yellow is on top. Recognition could be difficult at first but your brain will get used to it with practice.
Set up
Rw U' Rw' F R' U Rw' F' Rw F R U' R' F' R
Algorithm
?R'FRUR'F'Rw'FRwU'RF'RwURw'
R'FRUR'F'Lright → homeRw'FRwU'RF'RRwLright → underhandURw'
56-10
L embracing “counterclockwise edge”
How to recognize
In this example, the Red edge is considered a “counterclockwise edge” because in the standard color scheme, Red (color of edge embraced) follows Blue (color of L) in the counterclockwise direction when Yellow is on top. Recognition could be difficult at first but your brain will get used to it with practice.
Set up
Fw U R U' R' Fw' F U R U' R' U R U' R' F' U'
Algorithm
?(U)FRUR'U'RUR'U'SRUR'U'Fw'
(U)FRRUR'U'RUR'U'SRRUR'U'RFw'L
56-9
Checkmark embracing “clockwise edge”
How to recognize
In this example, the Orange edge is considered a “clockwise edge” because in the standard color scheme, Orange (color of edge embraced) follows Blue (color of checkmark) in the clockwise direction when Yellow is on top. Recognition could be difficult at first but your brain will get used to it with practice.
Set up
F U R U' R' U R U' R2 F' R U F' U F R U' R'
Algorithm
?RUR'F'U'FU'R'FR2UR'U'RUR'U'F'
RUR'F'LU'LFU'LR'FRR2UR'U'RUR'U'F'R
56-12
Checkmark embracing “counterclockwise edge”
How to recognize
In this example, the Green edge is considered a “counterclockwise edge” because in the standard color scheme, Green (color of edge embraced) follows Red (color of checkmark) in the counterclockwise direction when Yellow is on top. Recognition could be difficult at first but your brain will get used to it with practice.
Set up
F' Rw U' Rw' F2' Rw' F R F' Rw U2' R'
Algorithm
?RU2'Rw'FR'F'RwF2RwURw'F
RU2'Rw'FR'F'RRwLF2RRwURw'F
Class B2: The “empty dumbbell” (No L/checkmark)2 cases
Class B20/2 learnt
56-13
Clockwise edges
How to recognize
In this example, the Orange edge is considered a “clockwise edge” because in the standard color scheme, Orange (color of top edge) follows Blue (color of top-left corner) in the clockwise direction when Yellow is on top. Recognition could be difficult at first but your brain will get used to it with practice.
Set up
R' U2' R2' U R2' U R2' U2' R' U2' R' U' F R' F' R U R U'
Algorithm
?(U)R'U'R'FRF'URU2'RU2'R2'U'R2U'R2'U2'R
(U)right → underhandR'U'R'FRF'URRU2'right → homeRU2'R2'U'R2U'R2'U2'R
56-14
Counterclockwise edges
How to recognize
In this example, the Green edge is considered a “counterclockwise edge” because in the standard color scheme, Green (color of top edge) follows Red (color of top-left corner) in the counterclockwise direction when Yellow is on top. Recognition could be difficult at first but your brain will get used to it with practice.
Set up
F U R U' R2' F' R U2' R2' D R' U2' R D' R2'
Algorithm
?R2DR'U2RD'R2'U2'R'FR2UR'U'F'
right → overhandR2DR'U2RD'R2'U2'right → homeR'FR2UR'U'F'R
Group C · One Pair of Horizontally Matching Corners
Group C0/12 learnt
Class C1: With a 3x1 bar3 cases
Class C10/3 learnt
56-24
Left 2x1 bar
Set up
R' U' R U' R' U R F R' U R2' U' R' F' U2
Algorithm
?(U2)FRUR2'U'RF'R'U'RUR'UR
(U2)FRULR2'U'RF'R'U'LRUR'ULR
56-23
Right 2x1 bar
Set up
F R' F' Rw U R U' Rw' F U R U' R' F'
Algorithm
?FRUR'U'F'RwUR'U'Rw'FRF'
FRRUR'U'RF'LRwUR'U'Rw'FRF'
56-27
No 2x1 bar “The One Bar Case”
Set up
R U2' R' U' R U' R' U' F R U' R' U R U2' R' U' F'
Algorithm
?FURU2'R'U'RUR'F'URUR'URU2'R'
FRURRU2'R'U'RUR'F'URRURR'URRU2'R'
Class C2: With a 2x1 bar4 cases
Class C20/4 learnt
56-18
Adjacent headlight + left 2x1 bar
Set up
R U2' R' U' R' F' U' F U R U' R U' R' U
Algorithm
?(U')RUR'UR'U'F'UFRURU2'R'
(U')RUR'URR'U'F'RULFRRURRU2'R'
56-17
Adjacent headlight + right 2x1 bar
Set up
R' U2' R U2' F R U R' U' F' R' U R U
Algorithm
?(U')R'U'RFURU'R'F'U2R'U2'R
(U')R'U'RFRURRU'R'F'U2R'U2'R
56-21
Opposite headlight + left 2x1 bar
Set up
R U2 R' U F' U' F U2 R' F R' F' U
Algorithm
?(U')FR'F'RU2F'UFU'RU2'R'
(U')FR'F'RRU2F'URFRU'RU2'R'
56-22
Opposite headlight + right 2x1 bar
Set up
F' U2' F U' R U R' U2' F R' F' R
Algorithm
?R'FRF'U2RU'R'UF'U2F
R'FRF'U2RU'R'UF'U2RFR
Class C3: Single headlight only (no bars)5 cases
Class C30/5 learnt
56-28
Opposite headlight only
Set up
R' F' U' F R U R2' F' R U R U' R' F U R U
Algorithm
?(U')R'U'F'RUR'U'R'FR2U'R'F'UFR
(U')right → underhandR'U'RF'RUR'U'R'FR2U'R'F'URFRR
56-20
Left 5-piece checker
Set up
R' U' R F U' R' U2' R U2' R U' R' F' U2
Algorithm
?(U2)FRUR'U2'R'U2'RUF'R'UR
(U2)FRRUR'U2'R'U2'RUF'R'ULR
56-19
Right 5-piece checker
Set up
Rw U R U' Rw' F R' U R U' R' F' U2
Algorithm
?(U2)FRUR'U'RF'RwUR'U'Rw'
(U2)FRRUR'U'RF'RRwLUR'U'Rw'
56-26
Left 4-piece checker
Set up
Fw R' F' R U R U' R' F U R U' R' Fw'
Algorithm
?FwRUR'U'F'RUR'U'R'FRFw'
FwLRUR'U'RF'LRUR'U'R'FRFw'L
56-25
Right 4-piece checker
Set up
R' F' U2' F R U' R' U R U2' R' U R U' R' U R U
Algorithm
?(U')R'U'RUR'U'RU2R'U'RUR'F'U2'FR
(U')R'U'RUR'U'RU2R'U'RUR'F'RU2'FRR
Group D · One Pair of Vertically Matching Corners
Group D0/12 learnt
Class D1: Two 2x1 bars1 case
Class D10/1 learnt
56-40
Two 2x1 bars
Set up
F Fw' R U R' F' Fw R' F R F' U F R' F' R U
Algorithm
?(U')R'FRF'U'FR'F'RS'RU'R'S
(U')R'FRF'U'LFR'F'RRS'LRU'LR'S
Class D2: L/Checkmark6 cases
Class D20/6 learnt
56-35
L + 2x1 bar
Set up
Rw U R' U R U Rw' F U F R U' R' F'
Algorithm
?(U')RFwRFw'U2LUL'R'U2'LUL'
(U')right → overhandRFwRRFw'Lright → homeU2LUL'R'U2'right → homeLUL'
56-36
Checkmark + 2x1 bar
Set up
Fw' U' Fw U' R U2 R' U' R U2 R' U Fw' U Fw
Algorithm
?Fw'U'FwU'RU2'R'URU2'R'UFw'UFw
Fw'LU'LFwRU'LRU2'R'URU2'R'UFw'LURFwR
56-30
L embracing opposite edge
Set up
F' U' F Rw U' Rw' U Rw U' R' U' R U' Rw' U2
Algorithm
?(U2)RwUR'URURw'U'RwURw'F'UF
(U2)RwUR'URRULRw'U'RwURw'F'LURFR
56-29
Checkmark embracing opposite edge
Set up
Fw R Fw' Rw' U Rw U' Rw' U R U R' U Rw U2
Algorithm
?(U2)Rw'U'RU'R'U'RwURw'U'RwFwR'Fw'
(U2)Rw'U'RU'R'U'RwURw'U'RwFwRR'Fw'L
56-32
L embracing adjacent edge
Set up
Fw R U' R' U2' R' F' R U2' R U2' R' F U' Fw'
Algorithm
?FwUF'RU2'R'U2'R'FRU2'RUR'Fw'
FwRURF'RU2'R'U2'R'FRU2'RUR'Fw'L
56-31
Checkmark embracing adjacent edge
Set up
F' R2 U' F U R2 U R' U R' F' R2 U2 F
Algorithm
?F'U2'R2'FRU'RU'R2'U'F'UR2'F
F'RU2'right → underhandR2'FRRU'RU'R2'U'F'RULright → underhandR2'F
Class D3: One 2x12 cases
Class D30/2 learnt
56-37
Top 2x1 bar
Set up
Rw U Rw' U R U' R' Rw U' Rw' U R U' L' U R' U' L U2
Algorithm
?(U2)Rw'FRF'RwUR'U'RwUMUR'U'RwU'Rw'
(U2)Rw'FRRF'RwUR'U'RwUMLUR'U'RwU'Rw'
56-38
Bottom 2x1 bar
Set up
F2 R2 F U2 F U' R U R' U2 F2 R2 F' R' F' R
Algorithm
?R'FRFR2'F2U2'RU'R'UF'U2'F'R2'F2
right → underhandR'FRRFRR2'F2U2'RU'R'ULF'RU2'right → underhandF'RR2'F2
Class D4: No 2x13 cases
Class D40/3 learnt
56-39
Opposite Opposite
Set up
R' U' R U' R' F R' F' R U' R U' R' U R U R' U' R
Algorithm
?R'URU'R'U'RUR'UR'FRF'RUR'UR
R'ULRU'R'U'RULright → underhandR'UR'FRF'RUR'URR
56-33
Top Opposite
Set up
R U R' U R U2' R' F U F' R' F R U' R' F' R U2
Algorithm
?(U2)R'FRUR'F'RFU'F'RU2'R'U'RU'R'
(U2)R'FRUR'F'RFU'F'RRU2'R'U'RU'R'
56-34
Bottom Opposite
Set up
F R U' R2' U2' R U2' R U2' R' U' F' R' U R U'
Algorithm
?(U)R'U'RFURU2'R'U2R'U2'R2UR'F'
(U)R'U'RFRURRU2'R'U2R'U2'R2UR'F'