Megaminx Solver

Entering 132 stickers or a Megaminx scramble

The solver opens on a 3D Megaminx that you drag round and paint sticker by sticker, the way you hold your puzzle. The Flat net tab shows the same stickers as two flowers of six pentagons: the front half around the green face with white above it, and the back half around light green with gray below it. Every face has a center, five edges and five corners, 132 stickers in all, and even the centers start blank. With twelve colors the shortcuts run from 1 to 9, then 0, - and =, and the counter under each color stops at eleven.

The solver expects the standard scheme, in which look-alike shades sit on opposite faces: white and gray, green and light green, red and orange, purple and pink, yellow and beige, dark blue and light blue.

Mixed the puzzle from solved with a written list of moves? Put it in the “Or type a scramble” field and press Apply scramble. It reads the competition format, rows of R++, R—, D++ and D— that each end in U or U′, as well as plain face turns such as BL or DR. Keep a space between the U that closes each row and the R that opens the next.

Why a Megaminx position can be impossible

Your colors are checked before any search starts, and the stickers involved are outlined on the net:

• Wrong color counts Each of the twelve colors must appear exactly 11 times.
• Impossible centers The centers never move relative to one another, so they must sit as on a real Megaminx.
• A missing or repeated piece Each two-colored edge and three-colored corner exists exactly once.
• A twisted corner or a flipped edge on its own, which turning cannot produce.
• Two pieces exchanged Each face turn cycles five edges and five corners, so a lone swap never happens.

A common cause is a single sticker painted in a look-alike shade, such as beige where yellow belongs.

How the Megaminx auto solver finds a solution

Once the colors pass, the puzzle is turned in memory so that white is up and green in front, and the position goes to the Megaminx search of cubing.js, an open-source puzzle library, which runs in your browser.

The search is built to always finish, not to be short: over 200 random positions its solutions averaged about 155 moves, the longest 170. That is about twice the 77 moves of a competition scramble, because each R++ or D++ in a scramble swings most of the puzzle at once, while a solution turns one face at a time. Before anything appears, the moves are replayed on the site’s own copy of your puzzle, and if they would not solve it you get an error instead of a wrong answer.

Megaminx notation in the solution

Megaminx notation gives each face its own name. With white on top and green in front, U is the top, F the front, L and R its neighbors, and BL and BR the back faces of the top half. Below, FL and FR sit under the front, DL and DR further round, B at the back and D at the bottom.

A letter alone turns that face a fifth of a turn clockwise as you look at it. A 2 makes it two fifths and an apostrophe reverses it, so R2′ is two fifths counter-clockwise. The move strip under the replay colors each tile like the face it turns, which helps with names such as DL or BR.

Following the solution on your real Megaminx

Hold your puzzle as the note above the replay says, white on top and green in front, and keep that grip to the last move. The solution turns bottom faces too, so check each colored tile before you turn.

Play runs the replay, Next move gives single steps, and Speed goes from 0.5× to 4×; a click on any tile of the move strip jumps there. With around 150 turns, work in short runs and compare your puzzle with the replay after each. Copy share link copies a link that reopens this position, and Play with this puzzle loads it into the Megaminx online simulator.

How to solve a Megaminx yourself, from the white star to the last layer

By hand, the Megaminx is a 3x3 with more faces, solved in the same layer-by-layer spirit:

1. The white star. Place the five edges around the white face, then its five corners.
2. The first two layers. Complete the ring of five faces around white, one edge and corner pair at a time, as in the 3x3 middle layer.
3. Face by face, downward. Keep finishing the faces below, which leaves the gray face for last.
4. The last layer. Beginners solve it in four stages: flip the edges so gray forms a star, cycle those edges into place, cycle the corners into place, then twist the corners.

Many of the last-layer algorithms are adapted from the 3x3 beginner method. If a cube is new to you, start with the Rubik’s cube solver and its step-by-step mode, which shows the same ideas on a smaller puzzle.