Assume that a 10-D base cuboid contains only three base cells: (1) .a1, d2, d3, d4, :::,
d9, d10/, (2) .d1,b2, d3, d4,:::, d9, d10/, and (3) .d1, d2, c3, d4,:::, d9, d10/, where a1 6D
d1, b2 6D d2, and c3 6D d3. The measure of the cube is count( ).

(a) How many nonempty cuboids will a full data cube contain?
(b) How many nonempty aggregate (i.e., nonbase) cells will a full cube contain?
(c) How many nonempty aggregate cells will an iceberg cube contain if the condition of the iceberg cube is “count ≥ 2”?
(d) A cell, c, is a closed cell if there exists no cell, d, such that d is a specialization of
cell c (i.e., d is obtained by replacing a ∗ in c by a non-∗ value) and d has the same
measure value as c. A closed cube is a data cube consisting of only closed cells. How
many closed cells are in the full cube?