1. Cross
2. 2x2x1 block
3. 3x2x1 block
4. Final step
The 3x3x1 cube is actualy a cuboid, called Floppy Cube, based on a 3x3x3. In this type of cuboids the turns are always 180º, but we keep the number 2 in the notation because certain Floppy
cubes allow 90º without blocking. The pictures with red glowing shapes show what is intended, and the pictures on the very right show the final result (colouring just the well placed
pieces).
In this cuboid the center pieces are fixed. Therefore, in order to solve the cross we will have just two options: The cross is solved, or we need to turn the faces F, R, B or L to solve
it.
Let’s form a 2x2x1 block; in this tutorial it is created in the frontright part. In this step there are two possibilities, being the alreadysolved block one of them.
In Table 1 we have the possible positions for the corner of this 2x2x1 block, and the algorithms needed to get that block.
Table 1: Possible cases of the corner

L2 F2 L2 F2
F2 L2 F2 L2
F2 B2 L2 F2 B2
On the left there is no algorithm since the piece is well placed and oriented. In the rest of the cases the algorithm will be applied while holding the cube in the position shown in the
pictures. Those algorithms could be shorter but this way we keep the cross well placed.
Let’s create a 3x2x1 block that includes the previous one. We already have the cross, so the only remaining piece is the frontleft corner. There are three possibilities, being the
alreadysolved block one of them.
Table 2 shows the possible positions of the corner that completes the 3x2x1 block and the algorithms needed to get it.
Table 2: Possible cases of the corner

B2 L2 B2 L2
L2 B2 L2 B2
Like in the previous block, on the left there is no algorithm since the piece is well placed and oriented. In the rest of the cases the algorithm will be applied while holding the cube in
the position shown in the pictures.
This step is the easiest one because the two remaining corners get into their place automatically. There are two cases: In the first one the cube is solved; in the other one we have to turn
the B face to finish it.
By doing this, the cuboid is already solved. With some practice this cube can be solved intuitively and faster than using this method. We encourage you to try.