  Given a tiling of a 2D grid with several types of tiles, we can count for
every row and column how many tiles of each type it intersects. These numbers
are called the_projections_. We are interested in the problem of reconstructing
a tiling which has given projections. Some simple variants of this problem,
involving tiles that are 1x1 or 1x2 rectangles, have been studied in the past,
and were proved to be either solvable in polynomial time or NP-complete. In
this note we make progress toward a comprehensive classification of various
tiling reconstruction problems, by proving NP-completeness results for several
sets of tiles.
