Solve the Pyraminx

Hold the puzzle with one corner pointing up. Notation, if you want it: U, L, R and B mean turn the three pieces around that corner clockwise as you look straight at it, and a lowercase letter means turn only the little tip. A prime, as in R', means anticlockwise.

One. The tips. Each of the four tips twists on its own and affects nothing else on the puzzle, so you can solve all four at any time, in any order, just by twisting each until its colours match the corner beneath it. There are 81 ways the tips can sit and not one of them makes the rest of the puzzle harder. Get them out of the way first, or leave them until last; it makes no difference at all.

Two. The corners. Look at the four large corner blocks. They are already in the right places, because on this puzzle a corner cannot leave its vertex. Each one only needs twisting until its three colours match the three faces it sits on. Twist each corner in turn. When all four are right, the puzzle looks nearly finished and, importantly, you have not disturbed anything you will need later.

Three. The edges. This is the actual puzzle. Six edges, and you want them home the right way round. Most of them you can place by eye: turn a corner, notice which edge dropped into place, turn it back. Work around the puzzle placing edges one at a time, and keep going until either everything is solved or you are left with three edges that refuse.

For those last three, one short algorithm cycles them and leaves every corner alone: R' L R L'. Hold the puzzle so the three stubborn edges are the ones you want moved, play it, and look again. Its mirror, L R' L' R, cycles them the other way. Between them that is the entire memorised content of a Pyraminx solve. Each does one job and no more: three edges move, and all four corners come back untouched.

If an edge is in the right place but flipped, treat it as one of the three and cycle it out, then bring it back the other way round. The puzzle is small enough that fumbling works, which is exactly why it is a good first puzzle.

And there is genuinely little of it. Once the corners are right and three edges remain, only 12 arrangements can occur out of the forty-eight you might imagine. The flips always come in pairs and the shuffle is either nothing or a three-cycle, because those are the puzzle's two standing rules. Turning the puzzle in your hands does not make a new one, so what is left to recognise is 5 cases.