Let us say a set of $n$ rectangles is *rectifiable* if all $n$ rectangles together form a big rectangle without gaps or overlaps.

**Question:** How hard computationally is the question of deciding whether a set of $n$ rectangles with all dimensions integers is rectifiable?

If we further constrain the question by disallowing rotations of the tile rectangles OR by insisting that the longest sides of all rectangles should have same orientation in the layout, what happens?

Note: Analogous questions can be asked with sets of $n$ triangles and in higher dimensions.