The Square-1 is an interesting puzzle, and it’s solution is very unique. The concepts of other twisty puzzles can be applied to it, however it is special that corners and edges are indistinguishable to the puzzle’s inner mechanism- meaning corners can be swapped with edges and therefore the puzzle can change shape.
On the top and bottom layers of a Square-1 are thin (30o edge pieces) and thick (60o corner pieces) pieces. Every number in the algorithm means the multiple of 30o See the examples below for some rotations. For more information see the Rubik’s Notation page.
/ – a slice is like a 180o R rotation on the Rubik’s Cube.
(1,0)/ – rotate the top layer 30o clockwise and slice (like R on the Rubik’s Cube)
(0,2)/ – rotate the bottom layer 60o and slice
/(0,-1) – do a slice, then rotate bottom layer 30o counterclockwise then slice again
1. Bring the puzzle to a square shape
The Square-1 is much easier to work with when it is in the shape of a cube so this is going to be the first step to arrange the pieces so that the puzzle is cubic. After you’ve done that you can apply the algorithms to switch the pieces. There is no bad orientation of a piece because of the 180o slice.
Case 1: If every small piece is grouped
Case 2: If there’s a lonely small piece
To bring the cube to a square shape first you need to collect all the tiny pieces next to each other or leave maximum one lonely piece between two thick. This is not that hard to accomplish, it can be done intuitively, let that be the challenge for you. When this is done follow the steps on the pictures above. The black vertical line marks where to make the slice
If the middle layer is not square, apply this algorithm.
Now the shape of the puzzle is a cube, so we can easily handle the pieces. See the picture on the right to see the order of the pieces you have to switch. Find an explication and the algorithm for each step below.
2. Solve the top (yellow) corners
First bring all the corner pieces to the corresponding layer. This is not so complicated, it can be done intuitively. Then to switch two yellow corner pieces on the right top of the cube apply this algorithm. Note that the color of the middle layer determines whether the yellow or white layer goes to the top.
3. Bring the edges to their layers
To switch two edge pieces move them to the right top and right bottom of the cube then do the algorithm. Repeat this until every edge gets to its layer. It doesn’t matter if they’re not on the exact final spot, just the layer counts. Now you can see the white and yellow faces solved.
4. Solve the white corners
In the second step we solved the yellow corners, now take care about the white (or bottom layer) corners. Repeat this algorithm as many times needed to switch two corner pieces on the front-bottom of the cube.
5. Permute the edges
Now every edge got to its layer now we have to put them to the right place. We can do this switching two pieces on the top and in the same time two in the bottom layer. The algorithm switches the right-top with the back-top edge and the right-bottom edge with the back-bottom edge.
6. Solve parity
If only two edge pieces need to be switched to finish the cube than you’ve got parity. Use this long algorithm to switch two edges (not two pairs) then go back to point 5.