The grid presented here 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.)

A number outside the grid indicates the sum of the products of consecutive groups of squares in that row or column. (As shown in the example.

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