International Mathematical Olympiad 2004 Problem 3

Define a "hook" to be a figure made up of six unit squares as shown below in the picture, or any of the figures obtained by applying rotations and reflections to this figure.

Determine all $m \times n$ rectangles that can be covered without gaps and without overlaps with hooks such that

• the rectangle is covered without gaps and without overlaps

• no part of a hook covers area outside the rectangle.