EN

Pyraminx solver

Paint your scrambled pyraminx and get the shortest possible solution: tip turns first, then never more than 11 layer moves, shown one at a time.

Your pyraminx

Pick a color, then tap the triangles on the net. Hold the puzzle with one face toward you (Front) and one flat on the bottom.

Or type a scramble
How to read the net
  1. Hold the pyraminx with one face toward you and one face flat on the bottom. Paint the face toward you as Front (F, the middle triangle of the net).
  2. Turn the whole puzzle a third of a turn so the face on your left comes to the front, keeping the bottom down: paint it as Left (L), the triangle sharing the net's upper-left edge with Front.
  3. Turn back, then a third of a turn the other way for Right (R).
  4. Tip the puzzle toward you to see the bottom, with the edge that was nearest you now at the top: paint it as Bottom (D), below Front on the net.

The corner triangles of each face are the tips, the three triangles next to each tip are center pieces, and the rest are edges.

How to use the pyraminx solver

This pyraminx solver gives the shortest possible solution for your puzzle. Hold your pyraminx with one face toward you and one face flat on the bottom (green in front and yellow underneath on a standard puzzle). Paint the net to match: the front face sits in the middle, the left and right faces are folded out beside it, and the bottom face is below. Press Solve and follow the moves one at a time; the corner to turn is circled on the net.

Your puzzle can have any four colors and any face on the bottom: the solver reads which way you hold it from the three-colored center pieces next to the tips, which never leave their corner.

Pyraminx notation (WCA)

ULRB: back corner(behind)FRONT FACE (GREEN), YELLOW ON THE BOTTOM

The WCA Regulations (12e) name the four corners as you hold the puzzle: U the top corner, L the front-left corner, R the front-right corner and B the back corner. A capital letter turns that corner together with the layer under it (two layers, everything above the dashed line for U); a lowercase letter (u, l, r, b) turns only the small tip. Without a prime the turn is a third of a full turn clockwise as you look at that corner from outside; with a prime (U') it goes counter-clockwise.

How the solver works

Ignoring the tips, a pyraminx has 933,120 positions. The solver builds a table of how many moves every one of them is from solved (a breadth-first search, a fraction of a second in the background) and then walks down that table, so the layer moves are always the fewest possible: never more than 11, and 7.8 on average for a random position. The four tips are separate: a tip turns with its layer moves, but it can always be lined up with its center piece in one tip turn, and tip turns do not disturb anything else. That is why the solution lists the tip turns first. A scrambled pyraminx needs at most 15 moves in all, tips included.

Before solving, the solver checks your colors: 9 triangles of each color, four different center pieces with their colors in the right order, each tip matching the center piece under it, and six different edges. It also catches the two mistakes turns can never produce: a single flipped edge and two swapped edges. The triangles involved are outlined.

Worked example

Scramble a solved pyraminx with U L' R B' L u r' and enter it (paint it, or type the scramble under "Or type a scramble"). The solver answers u' r L' B R' L U': the two tip turns first, then five layer turns. Five is the minimum for the layers here, which is why the solution undoes the scramble exactly.

Tips

  • Paint the center pieces (the three triangles right under each tip) first. They never move to another corner, so they tell you where every color belongs.
  • A tip can be painted in any of its three turns; just make sure its colors go round the same way as the center piece under it.
  • Keep the bottom face flat on the table while you turn; it makes it easy to find the four corners again after each move.

Solver tested . Found a problem? Tell us.

Questions

How many moves does a pyraminx need?

At most 11 layer moves plus up to 4 tip turns, so 15 at most. A random position needs about 8 layer moves. This solver always finds the minimum number of layer moves and never uses more tip turns than needed.

What is the difference between U and u on a pyraminx?

A capital letter turns two layers: the corner tip and the layer under it with its three center pieces and edges. A lowercase letter turns only the small tip at the very top of that corner.

Why are the tip moves listed first?

Tip turns do not affect any other piece, so they can be done at any moment. Lining the tips up first makes the rest of the solution easier to follow because every center piece is easy to recognize.

The solver says an edge is flipped. What did I do wrong?

Turns always flip edges in pairs, so one flipped edge alone cannot happen on a real puzzle. Most often the two colors of one edge were painted the wrong way round; check the outlined edges. If your puzzle really has one flipped edge, it was taken apart and reassembled.

Does the solver work for the Master Pyraminx or the Pyramorphix?

No. It solves the standard pyraminx (three triangles per edge, 9 per face) used in WCA competitions.

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