All events · 4x4x4 Cube · Practise · Algorithms

4x4 · Beginner

Reduction: centres, then edges, then solve it like a 3x3, then fix parity. A first solve, about 10 to 20 minutes.

Move sequences on this page are only checked to be legal moves for this puzzle in cubing.js. Treat them as demonstrations of the notation and the method, not as verified algorithm lists. Both parity algorithms above were additionally simulated: each leaves all centres unchanged and keeps every edge paired. The first flips one edge pair, and the second swaps two edge pairs and touches nothing else.

How the 4x4 works

The 4x4 has no fixed centres: each face has four centre pieces that move. The plan is reduction: group the centres, pair up the edges, and the cube then behaves like a big 3x3.

Wide moves turn two layers at once: Rw is the right two layers, Uw the top two. An inner slice move such as 2R turns only the second layer from the right.

Rw U Rw' — a wide move, a top turn, and the wide move undone

2R U 2R' — the same idea with a single inner slice

1. The centres

Build one face's four centres as a 2x2 block of one colour, then the opposite face. Finally build the four ring faces. The colour scheme is fixed by the corners, not the centres, so when you place the last four, check against a corner piece: going around a corner the three colours must appear in the same clockwise order as on a real cube.

Work with the face you are building on one side and bring the other pieces next to it with a slice move, then put the slice back. The trick is always the same: set a piece up, do the inner slice that carries it, undo the setup.

2. Pairing the edges

Each edge on a 3x3 is two wing pieces here. Pair them up so that every edge looks like a single piece. Keep the paired edges on the same side (for instance the back), and bring unpaired wings to the front-right slot where a wide turn joins them.

Pair the first edges freely. The last few need care, because a careless move breaks pairs you have already made. If you cannot find a clean pairing, use a short algorithm to move a wing out of the way and pair another.

3. Solve it like a 3x3

Treat the paired edges as one piece each. Solve the cross, the first two layers and the last layer with the 3x3 beginner method. Only use outer-layer moves from here on.

4. Parity

On the 4x4 you may reach a last layer that the 3x3 method cannot solve. These are the two parity cases, and they only arise on even-sized cubes. In the flipped-edge case, one edge (or an odd number of edges) is flipped in the last layer. In the swapped-edge case, two edges are swapped and nothing else is wrong.

Fix the flipped edge with the first algorithm: it flips one edge pair and also moves two other edges and two corners, so afterwards continue with the 3x3 last layer as usual. Fix the swapped edges with the second algorithm: it swaps two opposite edge pairs of the top layer and changes nothing else, so afterwards solve the last layer as a normal 3x3 last layer.

Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw' — OLL parity: flips one edge pair, centres and the other pieces stay reduced

2R2 U2 2R2 Uw2 2R2 2U2 — PLL parity: swaps the front and back top edge pairs, nothing else changes