How to optimally place a cube on a flat sheet?

Question

Geometry

Hello!
There is a sheet of aluminum 1000x2000x1mm, it is necessary to make the maximum number of cubes 30x30x30mm from it.
Cube sweeps, all types:

That is, we impose a grid with a square with a side of 30 mm on an aluminum sheet, plus 0.5 mm on a hacksaw blade and we can use all these 22 types of cube sweeps.
The question is how to place these reamers as efficiently and optimally as possible in order to ensure the maximum output of cubes from one sheet?
Are there any programs, online services where you can count complex shapes, or some way to manually compose such a pattern?
Thank you!

Answer 1

I can offer a couple of options based on the best scans in my opinion (because they fit well with themselves):
The first option is 352 pcs. per sheet:
Second option - 336 pcs. on the sheet:
True, they are placed without taking into account the cut of 0.5 mm. I don’t know how you will cut them, but when bending into cubes, there will still be displacements and bends. You won't get completely perfect cubes. This cut can be neglected.
But it's up to you to decide.

Answer 2

Develop Tetris with such "details", upload it to Google Play, collect statistics - profit.