  In this paper, we deal with a simple geometric problem: Is it possible to
partition a rectangle into $k$ non-congruent rectangles of equal area? This
problem is motivated by the so-called `Mondrian art problem' that asks a
similar question for dissections with rectangles of integer sides. Here, we
generalize the Mondrian problem by allowing rectangles of real sides. In this
case, we show that the minimum value of $k$ for a rectangle to have a `perfect
Mondrian partition' (that is, with non-congruent equal-area rectangles) is
seven. Moreover, we prove that such a partition is unique (up to symmetries)
and that there exist exactly two proper perfect Mondrian partitions for $k=8$.
Finally, we also prove that any square has a perfect Mondrian decomposition for
$k\ge 7$.
