4x4 Rubik's Cube Solver (Rubik's Revenge)

Entering 96 stickers or a 4x4 scramble

A 4x4 has no fixed centers: the four middle stickers of each face sit on separate pieces that travel between faces whenever an inner layer turns. So the solver starts completely blank and asks for all 96 stickers, middle ones included. Pick a color with the mouse or keys 1 to 6; the counter under each swatch runs from “16 left” down to Done. The Flat net tab shows all six faces at once, and Fill solved helps when your cube is only a few turns from solved.

If you mixed the cube from solved with a written sequence, open the Scramble tab and press Apply scramble instead. It understands the notation 4x4 scrambles use: outer turns such as R′ or U2, wide turns such as Rw or 3Rw (a lowercase r means the same as Rw), and inner slices such as 2R. Rotations and the 3x3 slice letters M, E and S are refused. There is no camera scan for the 4x4; that works on the 3x3 and 2x2 solvers only.

What the solver does: centers, edge pairs, then a 3x3 finish

Like most people solving by hand, the solver makes the 4x4 behave like a 3x3. The solution panel shows Reduction method and splits the answer into four headed stages:

1. Centers. It tries all 24 ways of holding your cube, keeps the one whose centers finish quickest, and builds them from exact lookup tables.
2. Pair the edges. Each step lines pieces up with at most two outer turns, then plays an eight-move sequence that cycles three edge pieces while centers and corners stay put.
3. Parity. It fixes the positions a 3x3 can never be in, explained below.
4. Finish it as a 3x3. The same two-phase search as the Rubik’s cube solver for the 3x3 finishes in at most 21 outer turns.

Each stage comes with a short explanation, so the solution doubles as a map of the method.

Parity steps in your solution

With the edges paired, the cube looks like a 3x3, yet it may be in a position no 3x3 can reach. The solver checks for two such cases and adds a fix for each one it finds:

• OLL parity, one edge pair flipped in place: 15 moves, 2R2 B2 U2 2L U2 2R′ U2 2R U2 F2 2R F2 2L′ B2 2R2.
• PLL parity, two edge pairs swapped: 6 moves, 2R2 U2 2R2 Uw2 2R2 2U2.

The Parity stage therefore holds 0, 6, 15 or 21 moves. In testing, each fix was needed in about half of all positions. People solving by hand usually spot parity on the last layer; the solver fixes it earlier, because its 3x3 search only accepts a position a real 3x3 could be in, so these moves may come while the top is still mixed.

When the 4x4 solver rejects your colors

Once no sticker is blank, the colors are checked as you paint, and Solve stays disabled until they describe a real cube. The message names the first problem and outlines the stickers involved: a color that does not appear exactly 16 times, a color owning more than four of the 24 middle stickers, an edge piece that cannot exist, such as white beside yellow, the same edge piece painted twice, or a twisted corner left by a cube that was taken apart.

There is no parity check at this point: any arrangement of the edge pieces can be reached by turning, so a correctly painted 4x4 is always solvable. The standard color scheme is required, with white opposite yellow, red opposite orange and green opposite blue.

Reading 2R and Uw2 in a 4x4 solution

A face letter alone is a clockwise quarter turn of that outer layer as you look at it, ′ reverses it and 2 makes it a half turn. Two extra forms appear before the 3x3 stage:

A number in front, as in 2R, turns only the second layer from that face; centers, edge pairing and both parity fixes rely on these slices. Uw2 turns the top two layers together. While you follow, the caption under each move adds “(inner layer)” or “(two layers)” whenever it is not an ordinary face turn, and Full screen shows one large move at a time. Grip the outer layer firmly during inner slices; that is where most slips happen.

How many moves the 4x4 solver needs

A 4x4 has about 7.4 × 10⁴⁵ positions, and nobody knows the shortest possible solution for all of them. This solver aims for a solution you can follow rather than the shortest one. Measured on 500 random positions, the answers averaged 96 moves, ranged from 70 to 121, and spent about half of that on pairing edges. The 3x3 stage is never more than 21 moves; the parity stage adds 0, 6, 15 or 21.

Play with this cube lets you play the 4x4 Rubik’s cube online from your exact position, and the guide on how to solve a 4x4 Rubik’s cube teaches the same four stages by hand.