  We consider the problem of coloring a grid using k colors with the
restriction that in each row and each column has an specific number of cells of
each color. In an already classical result, Ryser obtained a necessary and
sufficient condition for the existence of such a coloring when two colors are
considered. This characterization yields a linear time algorithm for
constructing such a coloring when it exists. Gardner et al. showed that for
k>=7 the problem is NP-hard. Afterward Chrobak and Durr improved this result,
by proving that it remains NP-hard for k>=4. We solve the gap by showing that
for 3 colors the problem is already NP-hard. Besides we also give some results
on tiling tomography problems.
