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4x4

The first 'big' cube that introduces concepts like reduction and parity.

Moderate
WCA event
4x4x4 Cube
Positions
7.4 × 10⁴⁵
Method
Reduction (Yau for speed)
Parity
OLL and PLL

Overview

The 4x4 has no fixed centers. Each face has a 2x2 block of center pieces, and each edge is split into two pieces that can be separated.

The standard way to solve it is reduction which means you solve the centers and pair the edges, then finish like a 3x3. Once that's comfortable, the Yau method (solve two opposite centers and three cross edges first) is the most popular way to get faster.

Because on larger cubes not every piece is unique, you can wind up with a situation a normal 3x3 can't like one edge flipped by itself (OLL parity) or two edges swapped (PLL parity). Just find the correct algorithm to fix the partiy issue.

Notation

Outer turns work like a 3x3. Big cubes add moves for inner layers. w means wide (several layers from the outside), and a number in front says how many layers or which one.

RRight face clockwise (as if you were looking at it)
R'Right face counter-clockwise. A ' always means the reverse turn
R2Right face twice. Direction doesn't matter
RwRight two layers together. Also written r
2ROnly the second layer from the right
UwTop two layers together. Also written u
xTurn the whole cube like R

Reduction

Beginner

Turn the 4x4 into a big 3x3: solve the centers, pair up the edges, then solve it like a 3x3. The 3x3 part uses only outer turns.

  1. 1. Centers

    Each center is a 2x2 block. Solve two opposite centers first (white, then yellow), then the four side centers one at a time.

    Build a bar of center pieces, then move it next to the finished part with a wide turn, put the bar in, and undo the wide turn. Use Rw and Uw moves so you don't break centers you've already done.

    With no fixed centers, you have to place the side centers in the right order yourself, which can be annoying. On a standard color scheme green is opposite blue (cool colors), red is opposite orange (warm colors). If yellow is on top (white on bottom) and blue is in front, then red goes on the right. You can reference a solved 3x3 if you forget, and if your color scheme is not standard none of this applies so good luck :)

    Tip: Get the last two centers right before moving on. it's easy to finish with two centers swapped.

    All six centers solved

  2. 2. Edges

    Each edge is 2 pieces that need to line up. Find pieces that belong together and bring them to the front left and front right edges, lined up so one slice turn would join them. The algorithm pairs both edges without breaking the centers.

    The last two edges work the same way, hold them at the front left and front right and use the same algorithm.

    Centers solved, every edge paired

    Pair two edges

    Dw R F' U R' F Dw'

    Pairs the front left and front right edges without breaking the centers

  3. 3. Solve it like a 3x3

    This is the fun part. Using only outer turns (R, U, F, etc.,) you can basically solve the cube like it's a regular 3x3 using whatever method you already know. Treat each center block as one center and each paired edge as one edge.

    Even cubes can end in two positions a 3x3 never can, called parity. If you see one, use the parity algorithms below.

Parity

Beginner

Two positions you'll only see on even cubes. Both come from the edge pairing step, and each has one algorithm.

  1. OLL parity

    During OLL you see one edge that looks flipped, or an odd number of flipped edges. Hold the flipped edge at the front of the top layer and do the OLL parity algorithm, then carry on with OLL.

    OLL parity

    Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'

    When one single edge looks flipped. Hold it at the front of the top layer. Important: this messes up the rest of the top layer, so do it before OLL!

  2. PLL parity

    During PLL you see two edges swapped by themselves, or a case that isn't in the 21 PLLs. Do the PLL parity algorithm to swap the front and back edges, then finish PLL.

    PLL parity

    2R2 U2 2R2 Uw2 2R2 Uw2

    Swaps the front and back top edges. (Finish with U2 to line the top back up)

Yau

Intermediate

The method most fast 4x4 solvers use. It solves the first centers and cross edges early, so the rest of the edge pairing happens without rotating the cube.

  1. Steps

    Solve two opposite centers (usually white and yellow). Pair three of the white cross edges and place them. Solve the last four centers. Pair and place the last cross edge, then pair the remaining eight edges with Uw and Dw slices while holding the cross on the left. Finish as a 3x3.

Algorithms

Parity algorithms

2

The cases these solve: one flipped edge, and two swapped edges.

OLL parity

Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'

When one single edge looks flipped. Hold it at the front of the top layer. Important: this messes up the rest of the top layer, so do it before OLL!

OLL parity (pure)

2R2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 2R2

Flips the front edge and leaves everything else as it was. (2R means only the second layer from the right)

PLL parity

1

Arrows show which edge pieces swap.

PLL parity

2R2 U2 2R2 Uw2 2R2 Uw2

Swaps the front and back top edges. (Finish with U2 to line the top back up)

Edge pairing

1

The one algorithm you need to pair edges.

Pair two edges

Dw R F' U R' F Dw'

Pairs the front left and front right edges without breaking the centers

Tips

  • ★Most of your time goes into centers and edges. Practice those on their own until you can do them without stopping to look.
  • ★Look for the next piece while you're placing the current one. On a 4x4 there's always something to look for.
  • ★Use the same 3x3 method you already know for the last step, or use steps from the beginner method if you're uncomfortable with turning the big cube sides.
  • ★Learn to spot parity during OLL and PLL so you don't waste time on a case that can't be solved.

Resources

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