In you picture the grid is 4x4.

If you want to find ALL possible configurations inside a 10x10 with 2x2 and 1x2 elements, I would say, that there would be A LOT of configurations. Maybe a number we cannot calculate (too many digits).

Or you want just to fill that space with random configuration and find some good for you?

Here's my first thoughts:

Again, as some other cases, iterative process.

(Conway's game of life, a cellular_automata-like process (?)... Install anemone.)

I would create 3 grids:

1 - grid of 100 values, cell's center points

these values can have more integer values like 0=free 1=occuped

2 - grid of 81 values, grid vertex points (excludig perimeter)

these values are where the center of 2x2 cells could be. 0=possible location 1=not possible location

3 - "grid" of 180 values, grid segment center, where 1x2 center could be

again 0 and 1

Then it's needed a "topology" between those 3 grids:

At each iteration those values updates each other by basing on placed cells and adjacent values.

At each iteration a new cell (random from A or B) is placed in a random possible location.

This is just my madness, and maybe I'm already far away from a result.

For sure a fasterst, simpler, smarter solution exists.