The white corners

Four holes in the white layer

The cross is in, but the gaps between its arms are empty. On this cube all four white corners are loitering in the top layer — they're highlighted. Once each one reaches its slot, the white face will be complete, and every side will have a bottom row of three stickers matching its center.

One technique does the whole job: the sexy move from chapter 2. All you need to know is where each corner goes and how many times to repeat the move.

It doesn't matter which corner you start with. Grab any white corner in the top layer — they're easy to spot, with a white sticker facing up or out to the side. You place the corners one at a time, and they don't get in each other's way.

Where a corner lives

Pick a corner and read its colors. This one is white, green and orange, so its slot is on the bottom where the white, green and orange centers meet: front right, bottom layer.

The routine never changes. First turn the top until the corner sits directly above its slot. Then turn the whole cube (y) so that the slot is at the front right. Yellow stays on top. The sexy move always works in the front right corner: the slot below, the corner right above it.

Here the corner is already hovering right over its home. All that's left is to see which way its white sticker faces.

And what if there are no white corners on top but the layer still isn't finished? Then a corner is stuck down below. We'll come to its rescue a little further on.

White facing right: one sexy move

This corner's white sticker faces right. Play R U R' U' once, and the corner dives into its slot and lands white side down. That's it.

Notice that the sexy move leaves the other white pieces alone: the cross and the neighboring corners stay put. In the entire bottom layer it touches just one slot, the front right. That's why you can place the corners one by one without fear of wrecking the ones you've finished.

Why does it work? R lifts the right side of the cube, cross edge and all, but R' puts it straight back down. In between, U can only carry off pieces in the top layer, and U' brings them back. Whatever R lifted, R' lowers again — except for the pieces that U managed to swap out along the way. On the bottom there's exactly one such piece: the front right corner.

White facing you: five times

This corner has its white sticker facing front, and one sexy move won't cut it. Follow the corner as the cube plays the sequence. After the first sexy move it dives down but sits twisted. After the second it pops back up, now with white facing up. After the fourth it's on top again, white facing right. The fifth sends it home.

That's the whole secret: every two sexy moves, the corner dives, resurfaces and twists by a third of a turn. The white sticker travels around a circle — front, up, right — and then home.

White facing up: three times

A corner with white facing up is partway round the same circle: up, right, home. So, three sexy moves.

Put it all together and you get the rule: right — one, up — three, facing you — five. But you don't actually have to count. Just repeat the sexy move until the corner settles into its slot white side down. You'll never need more than five.

A corner stuck on the bottom

Sometimes a white corner is already on the bottom but in bad shape: in someone else's slot, or in its own slot but twisted. Here the white-green-orange corner is home, but its white sticker faces front.

The fix is simple. Hold the cube so that this corner is at the front right on the bottom, and play one sexy move. The corner pops up to the top — in this case right above its slot, white facing up. From there, follow the rule: three more sexy moves.

If the corner stuck on the bottom belongs somewhere else, kick it out the same way, then turn the top to bring it over its own home.

Where people trip up

• Turning the top between sexy moves. The sequence is one unit, and the U' at its end is already built in. An extra turn of the top carries the corner out of the work spot.
• Working in the wrong corner. The sexy move only fills the front right slot. Turn the whole cube first so that the slot is at the front right.
• Flipping the cube over. Yellow always stays on top — we're building the white layer on the bottom.
• Giving up halfway through. In the middle of a sequence the cube looks broken. It's supposed to.
• Mixing up slots. The white-green-red corner belongs at the front left, not the front right. Before you start, check all three of the corner's colors against the three centers around the slot.

And the ultimate safety net: if you lose count, just keep going. Six sexy moves in a row put everything back as it was, so the corner is bound to pass through the right position.

Try it yourself: a corner on top

Three white corners are already home. The fourth, white-green-orange, is up on top but far from its slot. Turn the top to bring it directly over its home, check which way the white sticker faces, and play the right number of sexy moves.

Try it yourself: a stuck corner

This time the corner is in its own slot, but twisted. Pop it out with one sexy move, look at the white sticker and finish the job.

Next: the middle layer

The white layer is done. The white face is on the bottom, and each side has a bottom row of three stickers with a center of the same color above it. Together they make an upside-down T — remember that shape, you'll need it very soon.

A third of the cube is solved. Next up is the middle layer: four edges with neither white nor yellow on them. They call for two new algorithms, and the two are mirror twins.