Pyraminx Solver

When a child has scrambled a Pyraminx (the triangle-shaped twisty puzzle) and nobody can solve it, paint the colours of its four faces on the net and the shortest solution is turned move by move on a 3D model. The page also explains the standard notation and a beginner's method you can learn by hand.

How to use

1. Hold the real puzzle with one face towards you and one corner pointing up. On the net in the "Solve" tab the middle triangle is the front face; the left, right and bottom faces are unfolded around it.
2. Choose a colour under "Paint colour" and tap stickers on the net (or on the 3D model) until they match the real puzzle. Press "Clear all" to start from blank, or "Scramble" to practise.
3. Press "Find solution" to see the total number of moves and the list of moves. If a sticker was painted wrong, a sentence explains what does not fit.
4. Each press of "Next" turns the 3D model and the net by one move, and the sentence below names the layer and direction of the next move. "Previous" goes back, and tapping a move in the list jumps to that step.
5. To learn to solve it by hand, open the "Beginner's method" tab. "Show" next to each algorithm runs it from the solved state so you can see which pieces it moves.

How it works

• Notation: U, L, R and B turn the layer at the top, front-left, front-right or back corner (the tip and the row under it) 120° clockwise, as seen looking at that corner. A ' means counter-clockwise, and the lower-case letters u, l, r and b turn only the small tip.
• The solver uses a distance table built by a breadth-first search over all 933,120 positions without the tips (edge placements 360 × edge flips 32 × centre turns 81). The layer moves are therefore always the shortest possible, never more than 11. The tips add 0 to 4 separate moves.
• The colour layout is read from the centre pieces, so a puzzle with other colours works too: paint it with any matching set of colours. Your painted state and the speed setting are kept only in this browser.

How to solve a Pyraminx: a beginner's method in four steps

Step 1, tips: turn each of the four small tips so it matches the centre piece right under it. Tips do not affect any other piece, so this can be done at any time.

Step 2, centres: choose a colour for the bottom face (say yellow) and turn the three lower corner layers until all three centres show that colour on the bottom. The lower parts of the side faces then match on their own.

Step 3, the three bottom edges: bring an edge with the bottom colour into the top layer, hold the puzzle with its slot at the front-bottom, and insert it from the right with R U' R' or from the left with L' U L. If it goes in flipped, take it out and insert it from the other side.

Step 4, the three top edges: when the three pieces must move round, use a cycle algorithm such as L U L' U L U L'; when two pieces sit in place but turned over, use the flip algorithm. Every algorithm in the "Beginner's method" tab was checked with this tool's own simulation.

How to read Pyraminx algorithms

An algorithm is turned one letter at a time from left to right. R U' R', for example, means: front-right corner layer clockwise, top corner layer counter-clockwise, then front-right corner layer counter-clockwise. Clockwise is always judged while looking straight at that corner.

The most important rule is not to change how you hold the puzzle in the middle of an algorithm. The sentence under the "Next" button uses the same fixed hold, for example "Top-corner layer clockwise".

How many moves does a Pyraminx need

Without the tips a Pyraminx has 933,120 positions; with the four tips (3 × 3 × 3 × 3 = 81 ways) there are 75,582,720. Counting layer moves only, every position can be solved in 11 moves or fewer, and a randomly scrambled puzzle usually needs 7 to 9. Each tip needs at most one turn, so the tips add at most 4 moves.

Questions and answers

What do U L R B mean in Pyraminx notation

Each letter turns the layer at one corner (top, front-left, front-right, back) 120° clockwise as seen from that corner. A ' as in U' means counter-clockwise, and a lower-case letter as in u turns only the tip.

What is the fewest number of moves to solve a Pyraminx

Without the tips, every position can be solved in at most 11 moves. This tool always finds the shortest layer sequence from its distance table and lists the tip moves separately.

I painted every sticker but it says the puzzle cannot be solved

Usually one sticker has the wrong colour. The message names the corner or edge piece that does not fit, so compare those stickers with the real puzzle again.

My Pyraminx has different colours

That is fine. The colour layout is read from the centre pieces, so choose the closest colours and paint them in the same places as on the real puzzle.

What is the beginner's method for the Pyraminx

Four steps: solve the tips, solve the centres, insert the three bottom edges and solve the three top edges. The "Beginner's method" tab explains each step with verified algorithms.