  An $N$-dimensional parallelepiped will be called a bar if and only if there
are no more than $k$ different numbers among the lengths of its sides (the
definition of bar depends on $k$). We prove that a parallelepiped can be
dissected into finite number of bars iff the lengths of sides of the
parallelepiped span a linear space of dimension no more than $k$ over $\QQ$.
This extends and generalizes a well-known theorem of Max Dehn about partition
of rectangles into squares. Several other results about dissections of
parallelepipeds are obtained.
