  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? It was known to be
solvable by a greedy algorithm for bars (tiles of width or height 1), and
NP-hardness results were known for some specific tiles. This paper shows that
the problem is NP-hard whenever the tile is not a bar.
