Pyraminx Solver

How to enter your Pyraminx

Hold the Pyraminx with one face toward you and one corner pointing straight up. That face is the Front, the big middle triangle of the net. The net is the puzzle unfolded flat around it: the Left and Right triangles are the faces that meet the front along its left and right edges, and the Bottom triangle is the face it stands on. Each one is drawn as you see it from outside, sharing an edge with the front exactly as on the puzzle, so the stickers along a shared edge belong to the same piece.

Pick a colour and tap the stickers that show it. Every colour appears on nine stickers, and the counter turns red until it does. The middle pieces at each corner never leave it, so the solver works out the colour scheme from them; any colours work.

What the moves mean

Keep holding it the same way: corner U on top, L and R at the bottom left and right of the front face, and B at the back. A capital letter turns that corner's third of the puzzle, the tip together with the layer under it, one step clockwise as you look straight at that corner. A letter with a dash, U', turns it anticlockwise. A small letter, u, turns only the tip. The tips come first because they never affect anything else; after that, the stickers that are about to move are outlined on the net, and Step walks through the turns one at a time.

Why it is always the shortest solution

Leave out the four tips, which are each one turn from home at most, and a Pyraminx has 933,120 positions. That is few enough to work out how far every one of them is from solved, which the page does in a fraction of a second the first time you press Solve, and then to walk downhill from yours. Nothing is estimated, so there is no shorter solution than the one it gives. No position needs more than 11 turns plus the tips, and by the page's own count only 32 positions need all eleven.

Before it went up it solved a thousand random Pyraminxes in random colour schemes, and a brute-force search confirmed nothing shorter existed for each answer it checked.

When it says your Pyraminx cannot be right

A painted net that no real Pyraminx could show is nearly always one of three slips, and the solver says which. A flipped edge has its two colours the wrong way round. Two swapped edges cannot happen by turning, only by taking the puzzle apart. And a centre or tip with its colours going round the wrong way, or two edges with the same pair of colours, means a sticker is painted wrong.

More twisty puzzles, and a pyramid in wood

The same kind of shortest-solution solver handles the 2x2 cube, and the full-size cube has its own Rubik's Cube solver. Why these puzzles have exactly as many positions as they do is in the mathematics of the Rubik's Cube.

We do not make twisty puzzles, but we do make a pyramid of a different kind: the 2 Piece Pyramid, two identical pieces that make a pyramid, a classic that catches out far more people than two pieces should. There are more solvers on the puzzle tools page.