The Why Cube

Before you start

26 pieces, not 54 stickers

The secret to the whole cube: stop thinking about stickers and start thinking about pieces. There are three kinds, and each kind follows its own rules.

Because the centres never move, the centres decide where everything goes. The white-red-green corner belongs between the white, red and green centres. Always.

Before you start

Reading the moves

Each letter is a face: Right, Left, Up, Down, Front, Back. A plain letter means a clockwise quarter turn, as if you were looking straight at that face. A dash R′ means the other way. A 2 R2 means turn it twice.

Before you start

The four tricks behind every move

Here's the big problem with solving layer by layer: once part of the cube is finished, almost any turn wrecks it. Every move sequence in this method gets around that with one of these tricks.

Out and back

R … R′

Open a side, move something while it's open, close it again. The side comes back. Whatever you moved in the gap doesn't.

Steps 1, 2, 3, 5, 7

Set up, then undo

F (work) F′

Move pieces to where your move can reach them, do the move, then undo the setup.

Steps 1, 4

A, B, undo A, undo B

A B A′ B′

If A and B only share one spot, almost everything cancels out. Just a few pieces end up moved.

Steps 2, 6, 7

Repeat

(…) (…) (…)

Do any sequence enough times and the cube comes back to where it started. Try it below.

Steps 2, 7

R comes back after 4. R′ D′ R D comes back after 6. Remember that 6. It's the reason step 7 works.

White on top

The white cross

Goal: the four white edges on top, each one matching the centre on its side.

Tricks: Out and backSet up, then undo

Why it works

The centres never move, so they tell you where each edge belongs. The white-green edge goes between the white centre and the green centre.
Right now only the top matters. The middle and bottom can get as messy as you like, so use them as your workspace.
You can't spin an edge in place. To flip one, take it out one way and bring it back in from a different side.

White on top

The white corners

Goal: finish the whole white layer. Turn the bottom to bring a white corner under its home spot (front-right), then repeat R′ D′ R D until it's in.

Tricks: A, B, undo A, undo BRepeat

Why it works

R′ D′ R D opens the right side, turns the bottom, closes the right side, and turns the bottom back. Of all the pieces in the top layer, only the front-right corner changes. Your finished pieces are safe.
Each time through swaps the front-right top corner with the corner right under it. So after an odd number of runs the corner is on top, and after an even number it's back on the bottom.
Every two runs twist the corner by one notch, a third of a full turn. That's why the three ways the corner can face need 1, 3 or 5 runs. Six runs would bring it all the way back to where it started.

Flip the cube: yellow on top

The middle layer

Goal: put the four middle edges in. Turn the top until an edge's front colour matches its centre (an upside-down T), then send it right or left.

Tricks: Out and back

Why it works

Turning the cube over puts the finished white layer on the bottom. Now U is a free move: it never touches the bottom two layers, so you can use it to set things up.
The move has two halves. First it builds a pair: the edge plus the white corner that belongs next to it. Then it drops the pair into its slot together.
Every opening move (R, F′) gets closed again (R′, F). Watch the counter in the corner of the cube: the bottom gets disturbed and then comes back whole.

If no edge fits

If every top edge has yellow on it, a middle edge must be stuck in the wrong slot or flipped. Do the move once to pop it out into the top layer, then put it back in properly.

Yellow on top

The yellow cross

Goal: yellow facing up on all four top edges. The side colours don't matter yet. One move, F R U R′ U′ F′, held the right way.

Tricks: Set up, then undoOut and back

Why it works

The F at the start and F′ at the end are a setup and its undo. The middle part, R U R′ U′, lifts edges up through the slot on the right. An edge that drops into that slot from the front comes out on top flipped over.
That's why you have to hold it right: the line left to right, or the L at back-left. Those are the positions that send the wrong edges through the slot.
One honest correction to Ruwix: for the dot, doing the move three times in a row only works if you turn the top in between. After the first time, aim the L to the back-left.

The cube's secret rule #1

You will never see one or three yellow edges up.

Try to break this rule. Turn anything you like and watch the dots.

Flipped edges always come in pairs. Once the first two layers are done, the flipped edges are exactly the top edges without yellow up. So that number is always 0, 2 or 4, which gives you a cross, an L or line, or a dot. Nothing else is possible.

Yellow on top

The yellow edges

Goal: each yellow edge's side colour matches its centre. The move R U R′ U R U2 R′ U swaps the front and left edges.

Tricks: Out and back

How to use it

Turn the top until at least two edges match their centres. This is always possible.
If the two wrong edges are next to each other, hold them at the front and left and do the move.
If they're opposite each other, do the move once from anywhere. Now they'll be next to each other.

Why it works

Every R has a matching R′. The first R U R′ parks a pair from the bottom up in the top layer. The R U2 R′ brings it home. In between, the top layer gets shuffled, and that shuffle is the swap.

The cube's secret rule #2

You can't swap just two pieces.

Swapping two edges always swaps two corners too. That's why the yellow corners got scrambled. The next two steps fix them.

Yellow on top

Yellow corners: right spots

Goal: every yellow corner in its correct spot, even if twisted. U R U′ L′ U R′ U′ L moves three corners around and leaves the front-right one alone.

Tricks: A, B, undo A, undo B

Why it works

The move is really four chunks: A = U R U′, B = L′, then undo A, then undo B.
A only works on the right side. B only works on the left side. So down in the bottom layers they never touch the same pieces, and everything they disturb there is undone. Watch the counter go 0, 5, 10, 5, 0.
In the top layer, the only spot both A and B touch is the back-left corner. That one overlap is what's left over: three corners trade places, and nothing else moves.

How to use it

Find a corner that's in its right spot (its three colours match the three centres around it, twisted or not). Hold it at front-right.
Do the move. If the other three are still wrong, do it once more.
If no corner is in its right spot, do the move once from anywhere. Then one will be.

Yellow on top

Yellow corners: twist them

Goal: solve the cube. Hold an unsolved corner at front-right and repeat R′ D′ R D until it's fixed. Then turn only the top to bring the next one over.

Tricks: RepeatA, B, undo A, undo B

Why it works

This is the step 2 move, and you already know what it does. Two runs twist the front-right corner one notch. Four runs twist it two notches. No other top piece moves.
The bottom does get messed up. But two runs always make the same mess, and that mess cancels itself after three helpings: six runs, the number from the Repeat experiment.
That's why you must only turn the top in between. U doesn't touch the bottom, so the mess stays lined up and can cancel. Turn the whole cube or the bottom and it won't.

The cube's secret rule #3

Corner twists always add up to full turns.

You can't twist one corner by itself. Every twist has to be balanced by twists somewhere else. So in step 7, the total number of runs is always 6 or 12, never something in between. And 6 and 12 are exactly when the bottom heals. The cube's own rule guarantees the mess goes away.