The language of turns

Sheet music for the cube

A pianist doesn't write "press the third key left of the middle" — they write a note. The cube has its own sheet music. Around 1980 the mathematician David Singmaster suggested writing every turn as a single letter, and his notation stuck for good: 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, as if you were looking straight at it. For R, imagine peering at the cube's right-hand side: the face turns the way a clock hand moves. From the front, the right column rolls up and away from you.

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

Try it yourself: do an R.

The point-of-view rule

Here's where nearly everyone trips up. Look at the cube 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 view the bottom from below. And B, seen from the front, looks counterclockwise — you're looking at 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 rewind: U followed by U' changes nothing.

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

Try it yourself: counterclockwise

Turn the top face a quarter turn counterclockwise, as seen from above. From the front, that means the front row slides 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 quarter turns clockwise are the same as 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 for the whole course: hold the cube with your right thumb on the front and your index finger on top. Then your wrist does R and R', and a flick of the index finger does U and U'.

Meet the sexy move

You've just played the most famous sequence on the cube. English-speaking cubers call it the sexy move; some teachers, keeping things classroom-friendly, call it the right-hand trigger. Whatever you call it, it falls into two beats — R U there, 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, but only seven pieces have moved — the highlighted ones: four corners and three edges. The other nineteen haven't budged. 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 the cube back to where it started. The sexy move gets there in six rounds. The innocent-looking R U, on the other hand, has to be repeated 105 times before the cube comes home!

Remember this. 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 common 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 only need y: a rotation of the entire cube around its vertical axis, in the same direction as U. The centers travel too, so after a y the front face is orange, not green.

Where people most often go wrong:

• turning L, D and B "like R" — forgetting to look at each face from its own side;
• shifting their grip without noticing. Check the centers: yellow on top, green facing you;
• rushing. Play slowly at first and say the letters out loud. Speed comes on its own, but a single wrong move ruins the whole algorithm.

Next: the first step of the solve

You can read the recipes now. 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 takes almost no algorithms — just common sense and one simple rule.