The language of turns

Sheet music for the cube

Composers don't write "press the third key to the left of the middle." They write a note. The cube has sheet music too. Around 1980 the mathematician David Singmaster proposed writing every turn as a single letter, and his notation stuck: today you'll find it in textbooks and at competitions alike.

Each letter is simply the first letter of a face's name:

• U (up) — the top; yellow in our grip;
• D (down) — the bottom; white;
• F (front) — green;
• B (back) — blue;
• R (right) — orange;
• L (left) — red.

A face's name belongs to its position, not its color: R is always the face on your right.

One letter, one quarter turn

A letter on its own means a quarter turn of that face, clockwise when you look at it head-on. For R, imagine peering at the cube's right side: the face turns the way a clock's hands move. Seen from the front, the right column rolls up and away from you.

The highlighted pieces are the layer R turns: the nine pieces in the right-hand third of the cube. Everything else stays put.

Try it yourself: do an R.

The point-of-view rule

This is where nearly everyone trips up. Seen from the front, R pushes the right column up, but L pulls the left column down. They seem to turn in opposite directions! Yet both are clockwise. You just have to picture L from the left and R from the right.

The same goes for the other pairs. U sends the front row to the left and D sends it to the right, because we judge the bottom from below. And B looks counterclockwise from the front, because you're viewing the back face through the cube.

A handy check: R and L' turn the same way, and both columns go up. Tap R L' and see for yourself.

Primes and twos

A prime mark reverses a turn. U' (say "U prime") turns the top counterclockwise as seen from above; from the front, you'll see the front row slide to the right. Think of the prime as a rewind button: U followed by U' changes nothing.

A 2 means a half turn: R2, U2, F2. Direction doesn't matter here. Clockwise or counterclockwise, 180° lands you in the same place. A half turn counts as one move, not two.

Try it yourself: counterclockwise

Give the top face a quarter turn counterclockwise, as seen from above. From the front, you'll see the front row slide off to the right.

If you slip and do U instead, no harm done: two more turns the same way and you're there. Three clockwise quarter turns add up to one counterclockwise.

Your first algorithm

An algorithm is just a few moves in a row, read left to right like a word. R U R' U' means "right clockwise, top clockwise, right back, top back."

Play it yourself. And here's a tip that will serve you all through the course: hold the cube with your right thumb on the front face and your index finger on top. Your wrist then handles R and R', your right index finger flicks U, and your left index finger flicks U'.

Meet the sexy move

You've just played the most famous sequence on the cube. Cubers call it the sexy move. It splits into two beats, R U out and R' U' back, and before long your fingers will play it without asking you.

Now look at what it actually does. The cube seems wrecked, yet only seven pieces have moved, the highlighted ones: four corners and three edges. The other nineteen end up exactly where they were. The sexy move is a precision tool: it changes a little, and it changes it predictably. In chapter 4 it will put the white corners in place, and in chapter 6 it will hide inside another algorithm.

Six sexy moves, and nothing happened

Here's the cube after one sexy move. Play it five more times, and the cube solves itself.

It isn't magic. The cube has a huge but finite number of positions, so any algorithm repeated over and over must sooner or later bring it back to where it started. The sexy move gets there in six rounds. The innocent-looking R U, by contrast, takes 105 rounds before the cube comes home!

Keep this in your back pocket. If you lose count halfway through a run of sexy moves, just keep going: six in a row is the same as none at all.

Turning the whole cube, and classic mistakes

Sometimes you need to turn the whole cube in your hands rather than a single face. That's what the lowercase letters x, y and z are for. We'll need only y: a rotation of the entire cube around its vertical axis, in the same direction as U. The prime and the 2 work just as they do for faces: y′ turns the other way, and y2 is a half turn. The centers travel along, so after a y the front face is orange, not green.

The mistakes people make most often:

• turning L, D and B as if they were R, instead of viewing each face from its own side;
• letting their grip drift without noticing. Check the centers: yellow on top, green facing you;
• rushing. Play slowly at first and say the letters out loud. Speed will come on its own, but one wrong move ruins the whole algorithm.

Next: the first step of the solve

Now you can read the recipes. Every technique from here on is written in these letters, and you can tap any sequence in the text to watch the cube play it for you.

Time to solve for real. The method starts with the daisy: four white edges around the yellow center. It needs almost no algorithms, just common sense and one simple rule.