Square packing in a square

Imagine you have a big square that you want to fill up with a bunch of smaller squares. The goal is to fit as many small squares as possible into the big square without leaving any gaps or overlapping.

To do this, you need to start by figuring out the size of the small squares, known as the "packing density." This depends on the size of the big square and the number of small squares you want to fit inside.

Once you have determined the packing density, you can start arranging the small squares inside the big square. The best way to do this is by starting in one corner and working your way across in rows, like building a wall.

As you add more and more small squares, you will start to fill up the big square. But eventually, you will probably run out of space, and there will be gaps left over. This is where it gets tricky.

To fill these gaps, you need to rearrange the small squares that are already inside the big square. You can move them around, rotate them, and even flip them over to create new configurations that allow you to add more squares.

This process of rearranging and filling in gaps continues until you can't fit any more squares in the big square. At this point, you have achieved the maximum packing density for that size of square and number of small squares. Congratulations, you've successfully packed a square in a square!