Thuat toan PLL
PLL (Hoan vi Tang Cuoi) la buoc cuoi cung cua phuong phap CFOP. Sau khi OLL da dinh huong tat ca cac nhan mat tren, PLL sap xep lai cac manh vao vi tri da giai. Co tong cong 21 truong hop PLL.
Neu ban la nguoi moi bat dau, hay bat dau voi 2-Look PLL -- mot cach tiep can don gian chi can 6 thuat toan thay vi tat ca 21.
2-Look PLL
2-Look PLL chia buoc hoan vi thanh hai buoc nho hon:
- Hoan vi cac goc -- dat 4 goc vao vi tri dung (2 truong hop)
- Hoan vi cac canh -- dat 4 canh vao vi tri dung (4 truong hop)
Dieu nay co nghia la ban chi can hoc 6 thuat toan tong cong.
Buoc 1: Hoan vi cac goc
Look at the top layer corners. Check if any pair of adjacent corners belongs to the same side (matching headlights).
Adjacent Corner Swap
One pair of adjacent corners is already correct. Hold the solved pair at the back and apply:
Thuat toan: R U R' U' R' F R2 U' R' U' R U R' F'
This is the T-Perm -- it swaps the two front corners (and two edges, which we fix in step 2).
Diagonal Corner Swap
No adjacent corners match. Apply the Y-Perm to swap corners diagonally:
Thuat toan: F R U' R' U' R U R' F' R U R' U' R' F R F'
Buoc 2: Hoan vi cac canh
All corners are now solved. Look at the edges and determine which need to cycle.
Ua Perm (3-edge cycle clockwise)
Three edges need to cycle clockwise. Hold the solved edge at the back.
Thuat toan: M2 U M U2 M' U M2
Ub Perm (3-edge cycle counter-clockwise)
Three edges need to cycle counter-clockwise. Hold the solved edge at the back.
Thuat toan: M2 U' M U2 M' U' M2
H Perm (Swap opposite edge pairs)
Two pairs of opposite edges need to swap.
Thuat toan: M2 U M2 U2 M2 U M2
Z Perm (Swap adjacent edge pairs)
Two pairs of adjacent edges need to swap. Hold so the two pairs are front/right and back/left.
Thuat toan: M2 U M2 U M' U2 M2 U2 M'
PLL day du -- Tat ca 21 truong hop
Chi canh (4 truong hop)
These PLLs only move edges; corners are already solved.
Ua Perm
Edges cycle clockwise. The solved edge is at the back.
Nhan dang: One solved bar (edge + two corners) visible from the back.
Thuat toan: M2 U M U2 M' U M2
Ub Perm
Edges cycle counter-clockwise. The solved edge is at the back.
Nhan dang: One solved bar visible from the back; edge colors cycle the opposite direction from Ua.
Thuat toan: M2 U' M U2 M' U' M2
H Perm
Two pairs of opposite edges swap.
Nhan dang: Every side has the opposite color in the center edge. Checkerboard pattern on all four sides.
Thuat toan: M2 U M2 U2 M2 U M2
Z Perm
Two pairs of adjacent edges swap.
Nhan dang: Two adjacent sides each have the other's color in the edge position. No side is fully solved.
Thuat toan: M2 U M2 U M' U2 M2 U2 M'
Chi goc (3 truong hop)
These PLLs only move corners; edges are already solved.
Aa Perm
Three corners cycle. Headlights on the left side.
Nhan dang: Headlights on one side, the bar (3 matching stickers) is on the opposite side.
Thuat toan: x R' U R' D2 R U' R' D2 R2 x'
Ab Perm
Three corners cycle (opposite direction to Aa). Headlights on the right side.
Nhan dang: Mirror of Aa -- headlights on the opposite side.
Thuat toan: x R2 D2 R U R' D2 R U' R x'
E Perm
Two pairs of diagonal corners swap. No edges move.
Nhan dang: No headlights on any side. Each side has two different corner colors.
Thuat toan: x' R U' R' D R U R' D' R U R' D R U' R' D' x
Doi goc ke (6 truong hop)
These PLLs swap one pair of adjacent corners along with edge permutations.
T Perm
Nhan dang: Headlights on the front and back. The two non-headlight sides each have their colors swapped.
Thuat toan: R U R' U' R' F R2 U' R' U' R U R' F'
F Perm
Nhan dang: Headlights on one side only (front). The other three sides have no matching pairs.
Thuat toan: R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R
Ja Perm
Nhan dang: A solved 1x1x3 block on the left side. The right side has adjacent pieces swapped.
Thuat toan: x R2 F R F' R U2 r' U r U2 x'
Jb Perm
Nhan dang: A solved 1x1x3 block on the right side. Mirror of Ja.
Thuat toan: R U R' F' R U R' U' R' F R2 U' R'
Ra Perm
Nhan dang: Headlights on the front. Adjacent corner and edge swap on the right side.
Thuat toan: R U' R' U' R U R D R' U' R D' R' U2 R'
Rb Perm
Nhan dang: Headlights on the back. Mirror of Ra.
Thuat toan: R' U2 R U2 R' F R U R' U' R' F' R2
Doi goc cheo (4 truong hop)
These PLLs swap two diagonally opposite corners.
V Perm
Nhan dang: No headlights on any side. One side has a 2-color pattern where the edge matches one corner.
Thuat toan: R' U R' U' y R' F' R2 U' R' U R' F R F
Y Perm
Nhan dang: No headlights. One side has two matching corners but the edge between them is wrong.
Thuat toan: F R U' R' U' R U R' F' R U R' U' R' F R F'
Na Perm
Nhan dang: Two opposite sides are fully solved (a solved bar on each), but the other two sides have their pieces completely swapped.
Thuat toan: R U R' U R U R' F' R U R' U' R' F R2 U' R' U2 R U' R'
Nb Perm
Nhan dang: Mirror of Na. Two opposite bars but swapped differently.
Thuat toan: R' U R U' R' F' U' F R U R' F R' F' R U' R
G Perms (4 truong hop)
The G permutations are the trickiest to recognize. They move both one pair of adjacent corners and cycle three edges.
Ga Perm
Nhan dang: Headlights on the left. The front-right corner matches the right edge.
Thuat toan: R2 U R' U R' U' R U' R2 U' D R' U R D'
Gb Perm
Nhan dang: Headlights on the front. The back-left corner matches the left edge.
Thuat toan: R' U' R U D' R2 U R' U R U' R U' R2 D
Gc Perm
Nhan dang: Headlights on the right. The front-left corner matches the left edge.
Thuat toan: R2 U' R U' R U R' U R2 U D' R U' R' D
Gd Perm
Nhan dang: Headlights on the back. The front-right corner matches the right edge.
Thuat toan: R U R' U' D R2 U' R U' R' U R' U R2 D'
Meo nhan dang
Efficient PLL recognition is key to fast solves. Here are general strategies:
- Look for headlights -- a pair of matching corners on one side. This narrows down the case immediately.
- Count solved bars -- a bar is three matching stickers in a row (corner-edge-corner). Bars indicate specific PLLs.
- Check two sides -- looking at the front and right side is usually enough to identify the case.
- Learn opposite patterns -- many PLLs come in mirror pairs (Ua/Ub, Ja/Jb, Ra/Rb, Ga-Gd).
| What you see | Possible PLLs |
|---|---|
| 4 sides with headlights | H, Ua, Ub, Z |
| 2 opposite sides with headlights | T, F, Ja, Jb, Ra, Rb |
| 1 side with headlights | Aa, Ab, Ga, Gb, Gc, Gd |
| 0 sides with headlights | E, V, Y, Na, Nb |
Thu tu hoc
A recommended order for learning all 21 PLLs:
- 2-Look first: T, Y (corners) + Ua, Ub, H, Z (edges) -- 6 algorithms
- Adjacent swaps: Ja, Jb, F, Ra, Rb -- 5 more algorithms
- Corner-only: Aa, Ab, E -- 3 more algorithms
- Diagonal swaps: V, Na, Nb -- 3 more algorithms
- G Perms last: Ga, Gb, Gc, Gd -- 4 final algorithms
Practice recognition by scrambling, solving to PLL, then covering the cube and trying to identify the case from memory. Speed comes from instant recognition, not just fast finger tricks.