Max square size for unknown number inside rectangle

Question

If I have a set of tiles (squares) which can be any number and they are to fill a container (rectangle) of an unknown size how do I work out the maximum size of the tiles wi

Answer 1

This is a packing problem. Optimal solutions are hard to find. See for example Packing N squares in a square.

You can compute an (optimistic) upper bound by dividing the total surface by the number of squares: sqrt(width*height/n).