The grid above can be partitioned into 9 L-shaped “hooks”. The largest is 9-by-9 (contains 17 squares), the next largest is 8-by-8 (contains 15 squares), and so on. The smallest hook is just a single square. Find where the hooks are located, and place nine 9’s in the largest hook, eight 8’s in the next-largest, etc., down to one 1 in the smallest hook.

The filled squares must form a connected region. (Squares are “connected” if they are orthogonally adjacent.) Furthermore, every 2-by-2 region must contain at least one unfilled square.

The sum of the values in each of the connected shaded regions must be the same (there are 19 such regions).

The answer to this puzzle is the product of the areas of the connected groups of empty squares in the completed grid.