andrewknelson.com

No explanation, just a new notation and the minimal alg list needed to learn square-1.

Notation:
R = Move the right half of the puzzle 180 degrees (clockwise)
u = move the U slice clockwise one “notch” Could be either (1,0) or (2,0) by old notation depending on what piece is to the right of the U notch.
u2 = move the U slice clockwise 2 “notches” Only used if there are 2 edges to he right of the U notch.
U = move the U slice clockwise 90 degrees. (3,0) in old notation
u4 = (4,0) in old notation
u5 = (5,0) in old notation
U2 = 180 degrees, (6,0)

Method:
Cubeshape: R u d’ R’ U’ d4′ R u2′ D R u’ d’ R U’ R
M2: u R u’ d’ R’
single EO: d’ R U’ R’ u4 d R u4′ d’ R’ U R
J/J: R U’ R’ U D R D’ R’
N/J: R U R’ U’ R U R’ U’ R
Adj/adj: d R U’ R’ u d R u d’ R’
Opp/opp: u R u’ d’ R’ U2 R u d R’
Pure parity: R U’ R’ D R D’ R’ D R u R’ d R u’ R’ u4 R d2′ R’ d2 R u4′ d R U R’
Flip E Slice: R U2′ R U2′ R

I recognize PLL with a combination of “Blocks” and “Bars” A block is two or three connected pieces, like so:

A bar is a set of connected corners. I’ve put bars in red wherever possible. The term “bar” is taken from 2×2 PBL recognition, so a bar may or may not include the edge in between the corners. (If it does, it’s also a 1×3 block):

You can tell the permutation of a layer (and its parity) by comparing blocks and bars in most cases. I’ve included some lookahead information for square-1 permutation, but the recognition part applies equally to 4×4 PLL. Listed is which EP case each permutation goes to with a proper Vandenbergh solution, and then information on 1-look permutation if it applies.
The E/X/Q cases are difficult to recognize with this technique, so I’ve added some notes to the end of the page detailing how I recognize these cases.

Permutation	Recognition		Corner Permutation		Resulting EP	1-look Permutation
No parity:
U		+	J	=	U	J 1 J
Z		+	J	=	Z	N/A
H		+	J	=	H	N 1 N
A		+	J	=	U	J 2 J
T		+	J	=	U	J 4 J
Ga		+	J	=	U	N J
Gb		+	J	=	U	J N
J		+	J	=	Solved	J or J J or J N or N J
R		+	J	=	U	N/A
F		+	J	=	U	N/A
Y		+	N	=	U	J 5 J
V		+	N	=	U	N/A
N		+	N	=	Solved	N or J 6 J
E		+	N	=	Z	N/A
Parity:
Opp Edges		+	Solved	=	Opp	N/A
Adj Edges		+	Solved	=	Adj	N/A
O		+	Solved	=	O	N/A
W		+	Solved	=	W	N/A
Opp Corners		+	N	=	Opp	N/A
Adj Corners		+	J	=	Adj	N/A
K		+	J	=	Adj	N/A
P		+	J	=	Opp or Adj	N/A
B		+	J	=	Adj	N/A
D		+	J	=	Opp	N/A
C		+	J	=	W or O	N/A
M		+	J	=	W	N/A
S		+	N	=	Adj	N/A
X		+	N	=	O	N/A
Q		+	N	=	O	N/A

Notes on E/X/Q:
These are definitely the hardest to distinguish. The trick is to look at two edges, and the corner between them, and apply the 3-color rule. If there are 3 colors, that means EP is correct, so you have an E-perm. If there are 2 colors, you have an X, and if there are 4 colors, you have a Q.

E
X
Q