Teaching 2-Look PLL with just 4 algorithms

Learning it yourself? Read the learner version.

For teaching someone who has F2L and 2-look OLL, but no PLL algs yet. The aim is the smallest alg set that finishes the cube, trading move count for less to memorize.

The idea

Standard 2-look PLL needs about 6 algs (A and E or Y for corners, Ua, Ub, H, Z for edges). This version needs 4: T, Ua, H, Z. Ub is just Ua done twice, and T replaces the corner algs.

The cost is moves. T is 14 moves, so corners take up to 28 instead of about 9 to 17 with a dedicated alg. It's a good first PLL, not an endpoint.

Diagram key

Top-down view of the last layer, front at the bottom. Bars are side stickers. Arrows are where pieces need to go. Gray means ignore for now.

Sides: front right back left

The algs

T14 moves. Swaps the two right corners and the left and right edges (headlights on the left).R U R' U' R' F R2 U' R' U' R U R' F'

Ua11 moves. With the solved edge at the back, moves front to left, left to right, right to front. Run it twice for the reverse direction (Ub).R2 U R U R' U' R' U' R' U R'

H7 moves. Swaps front with back and left with right.M2 U M2 U2 M2 U M2

Z9 moves. Swaps front with left and back with right.M2 U M2 U M' U2 M2 U2 M'

M turns the middle slice like L. Any U turn between algs is an AUF.

Step 1: Corners

Corners count as solved when all four match their centers after a U turn. Edges are ignored. Headlights are two adjacent corners with matching stickers on one face.

Solved

Go to Step 2.

Headlights

Put them on the left, do T. One T solves every headlights case, whether it looks like an adjacent swap or a 3-cycle.

R U R' U' R' F R2 U' R' U' R U R' F'

No headlights

Do T from any angle. Headlights will now exist, then follow the headlights rule. Covers diagonal swaps and the E case.

R U R' U' R' F R2 U' R' U' R U R' F'

Worst case is 2 T-perms.

Step 2: Edges

Turn U so the corners match their centers, then read the edges:

SolvedAUF and done

One correctPut it at the back. Ua, and if it didn't solve, Ua againR2 U R U R' U' R' U' R' U R'

HEach edge shows the opposite face's colorM2 U M2 U2 M2 U M2

ZEach edge shows a neighbor's color. This alg swaps front/left and back/right. If yours are front/right and back/left, rotate the whole cube 90° first.M2 U M2 U M' U2 M2 U2 M'

Why it works

Corners: a U turn is itself a corner move, so "solved" means solved up to a rotation. That makes a 3-cycle exactly one T-perm from solved, and an adjacent swap too. A state with no headlights (diagonal swap or E) turns into a headlights state after any one T. I checked all 24 corner arrangements this way.
Edges: once corners are solved, the edge permutation must be even. That leaves 12 cases: solved (1), 3-cycles (8), and double swaps (3, which are H and the two mirror forms of Z). Ua and its repeat cover the 3-cycles, and a 90° cube turn covers the mirrored Z.
The alg effects were checked on a cube simulator.

Teaching sequence

T-perm first. Drill until it's fast and clean. It's used in almost every solve here.
Headlights recognition before adding anything else. Have them point out headlights on random cases.
Ua, then H and Z (M-slice grips take practice).
Full solves with the recipe, talking through each decision aloud.

Common mistakes

Checking edges during Step 1. They'll look wrong, and that's expected.
Putting headlights on the wrong side. T swaps the right two corners.
Skipping the U turn to compare corners with centers.
Doing Ua once when the 3-cycle goes the other way. Do it again.
Forgetting the final AUF.

Where to go next

A-perm first, since it replaces the repeated T. Then Y and E, then the rest of full PLL as cases come up.