4×4: Edge Pairing

Centers banked — skill two of two: edge pairing. A 4×4 edge slot holds two wing pieces: 24 wings, each with exactly one partner. Join all twelve pairs and the cube is, functionally, a 3×3.

One move does all the work

Slice out with Uw — the top two layers turn together. Watch the middle band:

Two things happen at once:

• The upper wings shift one slot around the cube — this is what carries a wing next to its partner.
• The top row of every side center shifts with them — your centers break.

That’s a loan, not damage. Uw' puts every center piece straight back — as long as every side face sits where it started when you close.

The pairing loop

1. Line up a match — place a wing and its partner on neighboring slots of the middle band so one slice drives them together.
2. Slice out — Uw. The pair joins.
3. Store it — lift the finished pair into the top or bottom layer, turn that layer to carry the pair aside, then lower the face again. The lift cancels, and an unpaired edge drops into the slot the pair left.
4. Repeat — line up the next match the same way, store again.
5. Slice back — Uw'. Centers restore; stored pairs survive.

Storage is safe by construction: a pair lying in the top or bottom layer has both wings in the same layer, so no turn — not even the closing Uw' — can split it.

The rhythm: 2, then 3–2–3

One slice per pair works but wastes moves. Chain instead — every stored pair frees the slot for the next unpaired edge, so one slice-out feeds several matches:

• First pass: 2 pairs. Learn the motion — join, store, join, store, close.
• Then 3–2–3. Three more passes: three pairs, then two, then three.

That’s ten edges. The last two are special.

The last two edges: the flip trick

With only two unpaired edges left there is no spare edge to feed the slot — storing stops working. New exit:

1. Bring both unfinished edges to the front of the middle band, one left, one right.

2. Slice out — Uw. Nothing joins yet — the slice stages the wings for the return trip. One front slot now holds one wing of each edge, mismatched.

3. Flip that edge in place — lift it out of the band, roll it over the top, and reinsert it into the same slot, side faces back where they started. Flipping swaps its wings between the two inner layers — each now sits in its partner’s path. There is an algorithm for exactly this, and it is worth learning as a string rather than improvising it every time:

   R U R' F R' F' R

   It turns the front-right edge over in place and moves the four top edges round by one, intact. Seven outer turns, nothing wide — so it cannot break a pair you have already made, and it means literally the same thing on a 5×5, where you will meet it again.

4. Slice back — Uw' completes both edges at once and snaps the centers home.

Twelve edges closed: six one-color centers, twelve fat edges, eight corners. Hold it like a 3×3 and solve. Along the way you should expect cases no 3×3 can produce — that’s parity, it’s normal, and it’s the next lesson.