  For integers $m_1,...,m_d>0$ and a cuboid $M=[0,m_1]\times ... \times
[0,m_d]\subset \mathbb{R}^d$, a brick of $M$ is a closed cuboid whose vertices
have integer coordinates. A set $H$ of bricks in $M$ is a system of brick
islands if for each pair of bricks in $H$ one contains the other or they are
disjoint. Such a system is maximal if it cannot be extended to a larger system
of brick islands. Extending the work of Lengv\'{a}rszky, we show that the
minimum size of a maximal system of brick islands in $M$ is $\sum_{i=1}^d m_i -
(d-1)$. Also, in a cube $C=[0,m]^d$ we define the corresponding notion of a
system of cubic islands, and prove bounds on the sizes of maximal systems of
cubic islands.
