The final twist

One twist to go

Every piece is in its place. Only one small thing is missing: a couple of corners have their yellow facing sideways. Here it's both corners on the right, front and back.

This step is the quickest to explain and the most nerve-racking to do. Hold the cube yellow side up and keep that grip to the very end. The corner you're working on goes at the top right front.

You'll never see just one twisted corner here, only two, three or four. By the end of the chapter, you'll know why.

The move: R′ D′ R D

R' D' R D

It's a cousin of the sexy move, but it works the right face and the bottom instead. Repeat it until the top right front corner's yellow sticker faces up:

• yellow facing right — twice;
• yellow facing you — four times.

This corner has its yellow on the right: two rounds of R' D' R D, and it's yellow side up.

As with the white corners, you don't have to count; just keep your eye on the yellow sticker. Every two repetitions, the corner dives down, pops back up and twists a third of a turn. No corner will ever need more than four.

Don't panic!

Now look underneath. The two layers you solved have turned into a mess. This is exactly where lots of people panic, start "fixing" the bottom, and lose the whole solve.

Don't fix anything. Don't rotate the whole cube, and don't turn the bottom except as part of the move. The mess is by design: the bottom is only on loan, and it will come back on its own if you see the job through. Between corners, the one thing you're allowed to do is turn the top.

Think of a surgeon laying instruments out on a side table: the clutter during the operation is part of the job. What matters is that everything is back in place when it's over.

The next corner

Turn only the top to bring the next twisted corner to the front right. Here one U does it: the back right corner rides around to the front.

Its yellow faces you, so that's four rounds of R' D' R D. And remember: every corner takes an even number of repetitions. After an odd one, the corner is down in the bottom layer rather than up top, and it's too early to move on.

The miracle

The last corner twists into place, and with it the whole bottom snaps back together. One finishing touch remains: turn the top to line it up. Here that's U'.

The cube is solved. Look back at what just happened. You turned only the right face, the bottom and the top, and never once tried to fix the lower layers. They came back on their own.

Why the bottom has to come back

Watch: six R' D' R D in a row, and the cube is back where it started, just as with the sexy move. Between rounds you turn only the top, and the lower layers don't notice those turns at all. As far as the bottom is concerned, all your work is just one long run of R' D' R D. If the total count is divisible by six, the bottom comes back.

And it is. Every two repetitions twist a corner by a third of a turn. Remember the first law from chapter 1? The twists of all the corners always add up to whole turns. So if the corners can be fixed at all, the number of thirds is divisible by three, and the total number of repetitions is divisible by six. If it weren't, your cube would be one of those "eleven out of twelve" that can't be solved.

The bottom had no choice but to come back. It's not a magic trick — it's math.

Where people trip up

• Rotating the whole cube between corners. Then R' D' R D starts working on different pieces, and the bottom won't come back. Bring the next corner in by turning the top, and only the top.
• Stopping on an odd repetition. At that moment the corner is down below. Keep going until it comes back up, yellow on top.
• Mixing up D' and D. The bottom turns both ways, and it's easy to slip. Say it to yourself as you look at the front: "right down, bottom left, right up, bottom right."
• Giving up at the sight of the mess. The mess is a sign that everything is going to plan.

And if you do slip and the bottom doesn't come back, don't despair. The method works from any position, so start over from the daisy. The second time goes faster than you'd think.

Try it yourself: finish the solve

Three corners are twisted here. Fix each one in turn, bringing it to the front right by turning only the top, and see the cube through to the end. Don't forget the final turn of the top.

What's next

You've come the whole way: the daisy, the white cross, the white corners, the middle layer, the yellow cross, its edges, the corners in place and the final twist. There's no cube you can't solve now.

From here on, it's all practice. Solve the cube again, and then again. After a couple dozen solves, your hands will start running the algorithms on their own, and you'll notice you're seeing pieces rather than individual stickers. Time yourself: with a little practice, a layer-by-layer solve usually takes one to three minutes.

And if you want to go faster, the next three chapters cover intuitive F2L. There the white corners and the middle-layer edges go in as pairs rather than one at a time, and the same two layers take only a little over a third of the moves.

That's the bridge to CFOP, the method champions use. It has the same sexy move and the same Sune, just in new roles. And the course ends with a chapter on God's number: in 2010 it was proved that any cube can be solved in twenty moves or fewer. We'll see how a computer worked that out.