4x4 Rubik's Cube Solver

How to Use the 4x4 Solver

1. Pick up your cube and hold it any way you like. Keep holding it that way until you're done. The side facing you is the front, and the side pointing up is the top.
2. Enter the colors. Pick a color, then click each sticker of that color on the net. On a phone, you paint one face at a time in the large grid: tap a face on the net (or use Next face) to choose it. For the right, back and left sides, turn the whole cube so that side faces you, with the same side still on top. For the top, tip the cube toward you, so the row nearest the back goes at the top of the grid. For the bottom, tip it up, so the row nearest you goes at the top. Each color appears exactly 16 times, and the palette counts down.
3. Press Solve. The solver checks that your cube is possible, then works out a solution in four stages.
4. Follow the moves one at a time, holding the cube the same way you entered it. Use ◀ and ▶ to step back and forth, press Play to watch the whole solve, or click a stage name to jump to it.

No cube in your hand? Press Random scramble to try it, or type a scramble like Rw U2 2R' F Uw' under Or type a scramble. Typed scrambles start from a solved cube with white on top and green in front.

How to Hold the Cube

A 3x3 has fixed center stickers that tell you which side is which. A 4x4 doesn't: its centers are four loose pieces per face, and they move. So the solver doesn't ask for a particular grip. It looks at your centers and picks the color for each side that already has the most center pieces in place, then solves toward that.

The one rule: don't turn the whole cube in your hands until you've finished the moves. If you lose track, enter the colors again.

The solver assumes the standard color scheme: white opposite yellow, green opposite blue and red opposite orange.

What the Moves Mean

The solution uses the same notation as WCA scrambles, plus one extra kind of move for a single inner layer. A letter on its own turns one outer face a quarter turn clockwise, as you look straight at that face. An apostrophe means counterclockwise, and a 2 means turn it twice.

The step-by-step player says every move in words too, and the 3D cube shows which layers turn. The Rubik's Cube notation guide explains the 3x3 letters in more detail.

How the Solver Works: Reduction

The solver uses the reduction method, the same plan most people use to solve a 4x4 by hand. It turns the 4x4 into something that behaves like a 3x3, then solves that 3x3. The solution is split into these stages, and the player marks where each one starts:

1. Centers. Each face gets its four center pieces in one color. The solver starts with plain turns while they bring several center pieces home at once, then finishes with short move sequences that swap three center pieces and leave every other center piece alone.
2. Edges. Each of the 12 edges of a 4x4 is made of two pieces. This stage joins every pair, so each edge acts like one 3x3 edge. It uses 3-cycles again, this time ones that move three edge pieces and nothing else except corners.
3. Parity, when needed. Some paired 4x4s can't be finished as a 3x3. The next section explains why, and how the solver fixes it.
4. 3x3 stage. Now only the outer faces turn, so the centers and the paired edges stay together. The solver from our 3x3 solver finishes the cube.

Before showing a solution, the solver replays every move on a model of your cube and checks that it ends solved. If it didn't, you would see an error instead of a wrong answer.

We tested the solver on 1,000 scrambles of 60 random moves each, counting every move, including each Rw and 2R, as one. Every solution was checked by replaying it. The solutions averaged 109 moves, and the longest was 136. Per stage, the averages were: centers about 33 moves, edges about 46, parity about 11 (counting a scramble without parity as zero) and 3x3 stage about 20. On the laptop that ran the tests, half took under 0.2 seconds and all of them under 0.4 seconds. A phone is usually slower.

Why the Solution Is Long

A solution of about a hundred moves is not the shortest one: it is built from repeated patterns, not searched for the fewest moves. This solver aims for something else: a solution that is right every time and comes in clear stages you can follow. Each 3-cycle is a short, repeatable pattern of 8 to 14 moves, so the solution has a rhythm you can check against your cube. If a stage goes wrong in your hands, use ◀ to step back, or jump to the start of the stage.

What Is 4x4 Parity?

After the centers and edges are done, a 4x4 can end up in two states that no 3x3 can have. Both are called parity. They come from the inner layers, which move the edge pieces in ways that no 3x3 move can match.

• OLL parity: one edge looks flipped, as if it had been turned around in place.
• PLL parity: two edges are swapped and everything else is right.

The solver checks for both after pairing the edges. For OLL parity it uses a 15-move algorithm that flips one edge and changes nothing else. For PLL parity it uses a 6-move algorithm that swaps two edges and also turns the top layer a half turn, which the 3x3 stage then puts right. Both are listed, with their sources, on the 4x4 parity algorithms page, where we checked them on a 4x4 model. Of the 1,000 test scrambles, 490 needed the OLL parity algorithm and 520 the PLL parity algorithm (some needed both), and 254 needed neither.

"This Cube Can't Be Solved": What It Means

A 4x4 that was only ever scrambled by turning can always be solved. If the solver says yours can't, a color was most likely entered wrong. The message says what it found, and the pieces involved are outlined in red:

• Wrong color count. Some color appears more or fewer than 16 times. The palette shows "too many" under it.
• Wrong center colors. The 24 center stickers must hold each color exactly four times.
• Impossible, mirrored or repeated corner. A corner shows two colors that sit on opposite sides of a real cube, its colors go around in the wrong order, or the same corner appears twice.
• Twisted corner. One corner is rotated in place. That only happens if it was twisted by hand.
• Impossible or repeated edge piece. Each two-color edge piece exists twice on a 4x4, as mirror images. If one of them appears twice, two stickers on an edge are probably swapped.

The check can't catch every mistake. Almost any arrangement of center colors is possible on a 4x4, so if two center stickers are swapped while entering, the cube still looks possible, and the solver solves the cube you entered, not the one in your hand. If the moves stop matching your cube, check the centers first.

Everything runs in your browser. Your cube's colors are never sent anywhere.

Want to Solve It Yourself?

The same stages work by hand: centers, edge pairing, a parity algorithm when needed, then 3x3 moves. See how to solve a 4x4 for a step-by-step guide, learn the 4x4 parity algorithms, and time your solves with the cube timer.

4x4 Solver FAQ