The perfect square placement problem (also called the squared square problem)
is to pack a set of squares with given integer sizes into a bigger
square in such a way that no squares overlap each other and all square borders
are parallel to the border of the big square. For a perfect placement problem, all squares have different sizes. The sum of the square surfaces is equal to the
surface of the packing square, so that there is no spare capacity.
A simple perfect square placement problem is a perfect
square placement problem in which no
subset of the squares (greater than one) are placed in a rectangle.