How to use the square-1 solver
This square-1 solver takes any position, including scrambled shapes, and gives a solution in WCA notation that brings it back to a solved cube. Instead of painting stickers you place pieces: look at the top layer, find the piece that starts at the front end of the cut, and tap the matching piece in the list. Keep going clockwise until the layer is full, then do the same for the bottom layer. Set the middle layer, press Solve and follow the moves.
- The cut is the line the / move turns along. Hold the puzzle so that it runs from front to back, with the half that turns on your right.
- Top layer: look down from above. Start with the piece just left of the cut at the front and go clockwise (to the left, round the back, down the right side).
- Bottom layer: tilt the puzzle toward you so you look at the bottom, with the front edge now at the top. Start again at the front end of the cut and go clockwise (to the right first).
- If a corner sits across the front end of the cut, turn that layer one notch before you start, so the cut runs between two pieces there.
The drawing shows each layer as you see it, with the dashed cut and an arrow at the starting point. Corners fill two notches, edges one, and each layer has 12 notches.
Square-1 notation (WCA)
The WCA Regulations (12c) write a square-1 solution as turns and slashes. (x,y) turns the top layer x notches clockwise as seen from above and the bottom layer y notches clockwise as seen from below; one notch is 30 degrees, and a negative number turns the other way. / turns the right half of the puzzle 180 degrees. The colors and starting position match the images of the WCA scramble program: yellow on top, red in front.
How the solver works
Square-1 changes shape as you turn it, so the solver works in two phases. The first phase uses a table of every shape (with the middle layer and a parity check) and finds the fewest slashes that bring the puzzle back to a cube. The second phase solves the pieces without leaving the cube shape, with an iterative deepening search guided by two tables that say how far the corners and the edges are from solved. The solver tries several first-phase routes and keeps the shortest result. Every solution is replayed on a model of the puzzle before it is shown, so it always ends solved and cube shaped, middle layer included.
The solutions are short but not always the shortest possible. In our test of 500 random positions they used between 7 and 16 slashes, 12.6 on average. Most take a fraction of a second to find; the slowest took under two seconds.
Worked example
From a solved puzzle, scramble with (1,0) / (-1,2) / (3,0) / (0,-3) / (type it under "Or type a scramble" to load it). The solver answers / (0,3) / (3,6) / (-2,1) / (5,6): four slashes, the same number as the scramble. Turning a layer 6 notches is half a turn, so (3,6) and (3,-6) are the same move.
Tips
- Count notches before you place pieces: a layer with more than 12 notches has a piece that belongs to the other layer.
- The middle layer is square when its two halves line up into a rectangle on every side; otherwise choose "Not square".
- After each slash, check that the cut is still where you expect. Turning the whole puzzle by accident is the most common way to lose your place.
Solver tested . Found a problem? Tell us.
Questions
What does (1,0) / mean on a square-1?
(1,0) turns the top layer one notch (30 degrees) clockwise as seen from above and leaves the bottom layer alone. The slash then turns the right half of the puzzle 180 degrees. The two numbers are always top first, bottom second.
Does the solver fix the middle layer too?
Yes. Tell it whether your middle layer is square or not, and the solution ends with the middle layer square and every piece in place.
Can it solve a square-1 that is not in cube shape?
Yes. Any shape is fine as long as all 16 pieces are placed. The first part of the solution returns the puzzle to cube shape, the second part solves the pieces.
Why does the solver say a layer is too full?
Each layer has 12 notches: a corner fills two and an edge one. If a layer adds up to more than 12, a piece from the other layer was added to it, or a corner was added twice.
Is this the shortest possible solution?
Not always. It is a two-phase solver: solutions are short (7 to 16 slashes in our tests) and always correct, but a slower exhaustive search can sometimes find one or two slashes fewer.
My square-1 has different colors. Can I still use it?
Yes. Use the piece list by position instead of color: match each of your pieces to the piece that sits in the same place on a solved puzzle held the same way.