  Inside a two dimensional region ("cake"), there are $m$ non-overlapping tiles
of a certain kind ("toppings"). We want to expand the toppings while keeping
them non-overlapping, and possibly add some blank pieces of the same "certain
kind", such that the entire cake is covered. How many blanks must we add?
  We study this question in several cases: (1) The cake and toppings are
general polygons. (2) The cake and toppings are convex figures. (3) The cake
and toppings are axes-parallel rectangles. (4) The cake is an axes-parallel
rectilinear polygon and the toppings are axes-parallel rectangles. In all four
cases, we provide tight bounds on the number of blanks.
