Discrete tomography deals with reconstructing finite spatial objects from
lower dimensional projections and has applications for example in timetable
design. In this paper we consider the problem of reconstructing a tile packing
from its row and column projections. It consists of disjoint copies of a fixed
tile, all contained in some rectangular grid. The projections tell how many
cells are covered by a tile in each row and column. How difficult is it to
construct a tile packing satisfying given projections?