Under this answer, user Bruno Joyal asks:
This might be a naive question, but... how do we know there is a best possible solution?
I (but that's just me) assume that he might be thinking of a logical possibility that there is a sequence of ever better solutions, but that the limit itself is not a solution. But, whether he is or not doesn't quite matter. So, here goes...
Can it be proven that there exists an optimal solution?
How big a square do you need to hold eleven little squares?
We don't even know if this is the best possible [solution.]