Something that can be difficult to fully grasp in the early stages of 3D design is the relationship between objects in 3D while looking at a 2D representation on a screen.  Like in Edwin Abbott's Flatland how can one even conceive of a third dimension when everything is just made up of lines? Luckily for us though, we are living in the third dimension so it is just a matter of visualizing our designs and practicing our spatial awareness(wait how many dimensions are there?). Hopefully learning how to fold a 2D design into a 3D box and designing your own 3D puzzle with some simple cubes will help.  

Visualizing the Puzzle in 2D

The first step to designing in 3D is to first draw a 2D sketch of a view of your design. These sketches are then extruded into the third dimension. So for this puzzle a good place to start is the complete lay out in 2D. 

If you look at the example on the side you can think of it as a 3x3x3 cube. Which means that you can break it down into 3 layers of blocks stacked on top of each other.  In 3D modeling (and math) these layers are called planes. We can visualize the planes that cut through the cube at these three levels in 2D with the example below which you can click on for your own copy

The 2D Sketch

Before jumping right into your 3D modeling software a good idea may be to sketch out some preliminary designs on paper. Each grid represents a level of blocks that when combined make up the 3x3x3 cube. This example layout enables you to be able to design a variety of different cube puzzles by coloring in blocks on the three levels with a few constraints:

Once you have an idea of what you want to model in 3D your next step is to design it in your parametric modeling software of choice. I chose to make each square .75in with the overall size being a 2.25in x 2.25in. This grid that you now have drawn is the same as the one of the layers you sketched above, but how do you make it 3 layers? 

The easiest way is to add new 2D planes to your design that will allow you to stack these grids on top of each other. With a plane offset of also .75in you can copy the grid sketch onto the other 2 planes to end up with something like this:

3D Parts

You've finished all the prep work and are now ready to turn your 2D sketches into 3D parts. As I said earlier, 3D CAD modeling software will take a 2D sketch and turn that into a 3D element. Depending on the software you use