The final twist

Only the twist is left

Every piece is in its place. Just 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 don't change your grip until 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. Why that is will become clear by the end of the chapter.

The move: R' D' R D

R' D' R D

It's a cousin of the sexy move, only this one works the right face and the bottom. Repeat it until the yellow sticker of the top right front corner 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.

Just as with the white corners, you don't have to count — keep your eye on the yellow sticker. Every two repetitions the corner dives down, pops back up and turns 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 touch the bottom. This is how it's meant to be: the bottom is only taken apart for a while, and it will come back on its own if you see the job through. The one thing you're allowed to do is turn the top.

Think of a surgeon laying instruments out on a side table: the mess during the operation is part of the job. What matters is that everything is back in place at the end.

The next corner

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

Its yellow is facing you — so that's four rounds of R' D' R D. And remember: every corner always takes an even number of repetitions. After an odd one, the corner is down at the bottom 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 solves itself. One finishing touch is left: turn the top so it lines up. Here that's U'.

The cube is solved. Look back at what just happened. We 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 like the sexy move. Between the rounds we turn only the top, and the lower layers don't notice those turns at all. As far as the bottom is concerned, all our work is simply a long run of R' D' R D. If the total number 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 by six. If it weren't, the 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: 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. Twist each one — bringing them to the front right spot by turning only the top — and see the cube through to the end. Don't forget the last turn of the top.

What's next

You've come all the 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. Any cube is yours now.

From here on, it's practice. Solve the cube again, then again. After a few dozen solves your hands will start doing the algorithms by themselves, and you'll notice you're looking at 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 chapter is about CFOP, the method champions use. It has the same sexy move and the same Sune, just in new roles. After that comes the 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.