CFOP — how the champions solve

Same cube, different speed

With the layer-by-layer method, a solve takes 100–150 moves. A speedcuber needs 55–60, and the best of them turn more than ten moves a second. Record solves in competition last about three seconds — less time than it takes you to finish reading this paragraph.

It isn't just nimble fingers. Most strong cubers solve with the same scheme, called CFOP after the initials of its four stages: Cross, F2L — the first two layers, and OLL and PLL — the last layer in two goes.

The method is often named after Jessica Fridrich, though she wasn't the only one who came up with it. In the early '80s, several cubers arrived at similar ideas: the cross on the bottom, corners paired up with edges, the last layer in two stages. Fridrich pulled them together into a complete system and, in 1997, posted a detailed write-up online. From there the method spread around the world.

Cross — planned in advance

In competition you get 15 seconds of inspection before the solve: you can turn the cube over in your hands, but you can't turn any layers. A champion spends them on the cross. They find the four white edges and plan the whole route, from the first move to the last. Then they build the cross almost without looking — by then their eyes are already hunting for what comes next.

No daisy here: each edge goes straight down to its own spot. A computer search shows that any white cross can be solved in at most 8 moves, and 5–7 is usually enough. This cube needs six: R' F2 D R' F D.

There's a reason the cross goes on the bottom. It keeps the top in view, and that's where the interesting part is about to happen.

F2L — columns instead of layers

In the layer-by-layer method, you put the white corners in one at a time, then drove the middle-layer edges home with separate long algorithms. F2L (First Two Layers) does both jobs at once. A corner and an edge meet up top, lock together into a pair and go down together — a whole column at a time. Four pairs, and two layers are done.

Here the pair has already formed: on top, the corner and the edge are both green, on the right both orange, and the corner's white sticker faces you. Inserting it takes four moves, U R U' R': move the pair aside, lift the slot, tuck the pair in, lower the slot. The white cross edge slips out of place for a moment, but the last move brings it home.

There's a mirror case too, where the pair lies along the front face. Then the same four moves work with the front face instead, and the top turns the other way.

When the pair builds itself

The corner sits right above its slot, white facing right, and the edge is on the far side of the top. Watch what the very first R does: it lifts the slot and, in the same motion, sets the corner right next to the edge. Pair made! Then a turn of the top brings the pair over the slot, and turning the right face back drops it in. Just three moves: R U R'.

F2L has 41 cases — that's how many different pictures the corner and edge of one pair can make. You could learn 41 algorithms, but almost everyone starts another way. They get three ideas — separate, join, insert — and work out the rest themselves. The ready-made algorithms come later, for speed.

Typical mistakes:

• Breaking the cross. If a move lifts a white edge, the same sequence has to put it back.
• Freezing while you search. Pauses between pairs cost more time than slow hands do. Better to turn slowly but never stop.

Try it yourself: insert the pair

The corner is in the far left corner of the top, and the edge is at the front. You can't insert the pair from here. First turn the top layer so the corner sits above its slot at front right. Recognize the case? From there it's the three moves from the last frame.

OLL — the whole top yellow

Two layers are solved; only the top one is left. OLL (Orientation of the Last Layer) turns all its pieces yellow side up — without caring yet where each one sits. The cube is showing only yellow right now, and that's exactly how cubers look at this stage too.

Full OLL has 57 cases, each with its own algorithm. To begin with, 2-look OLL is enough — two looks: first the yellow cross, then the corners. You already know the cross, only now there's one algorithm per case and no repeats:

• the line, running left to right — F R U R' U' F';
• the L-shape with its yellow edges on the right and at the front — f R U R' U' f'. Here f turns the two front layers together;
• the dot — both in a row, as on the cube: the first turns the dot into an L-shape, the second turns that into a cross.

Seven pictures for the corners

The cross is done — now for twisting the corners. There are only seven cases, and each has a name: Sune, Antisune, H, Pi, U, T, L.

On the cube is Sune, also known as the fish: just one corner on top shows yellow, and together with the cross it draws a fish. Hold it like this: the yellow corner at front left, and the yellow sticker of the front right corner facing you. The algorithm is R U R' U R U2 R'. Antisune is the mirror-image fish, and its algorithm is Sune played backwards: R U2 R' U' R U' R'.

Recognize Sune? In the layer-by-layer method, R U R' U R U2 R' U swapped two edges. That's the same Sune plus a turn of the top. One algorithm, two jobs: it moves edges around and it twists corners. Back then you needed the first job; now you need the second.

Try it yourself: the fish

There's a fish in front of you. Hold it as in the last frame and do Sune: first R U R' U, then R U2 R'. The bottom two layers will come apart for a couple of moves and snap back together, and the top will turn completely yellow.

PLL — everything in its place

The top is yellow, but the colors around the sides are jumbled. PLL (Permutation of the Last Layer) moves the pieces around without disturbing the yellow top. There are 21 cases, and each one is named after a letter: the arrows on the case's diagram look like that letter.

On the cube is the T-perm: the left and right edges trade places, and so do the two right-hand corners. The arrows form a letter T lying on its side. The algorithm is R U R' U' R' F R2 U' R' U' R U R' F'. Among the others: Ua and Ub cycle three edges, H swaps opposite edges, Z swaps edges in neighboring pairs, A cycles three corners, and J and Y swap corners along with edges.

2-look PLL gets by with six algorithms. Corners first. Look for "headlights" — a side where both corners have side stickers of the same color. Headlights on one side: put them on the left and do a T-perm. No headlights anywhere: Y-perm. Headlights on every side: the corners are already in place. Then the edges: Ua, Ub, H or Z.

In the layer-by-layer method the last layer took four stages: cross, edges, corners into place, corners twisted. CFOP does it in two: first orient everything, then put everything in its place.

Try it yourself: T-perm

Fourteen moves is a lot, but you learn it in chunks. The first chunk is an old friend, the sexy move R U R' U'. Next comes R' F R2 U' R', and the finale is U' R U R' F'. Three chunks in a row — and the cube is solved.

Fingers, eyes and what's next

A cuber's hands work like a pianist's. U is a flick of the index finger, R is a turn of the wrist, and the sexy move sounds like a short drum roll. These techniques are called fingertricks: the algorithm is played without ever regripping the cube.

But the real speed is in the eyes. While your hands insert one pair, your eyes are already looking for the next. A cuber who turns slowly but never pauses will beat one who rushes ahead and then freezes.

Where to start? With 2-look, which is about fifteen algorithms: 9 for OLL (the dot is just two familiar ones in a row) and 6 for PLL. Then, one at a time, the full sets. All 57 OLL and 21 PLL cases are in the algorithm library, with diagrams and animations.

And in the next chapter: why any position of the cube can be solved in twenty moves or fewer, and how we found out.