Twenty Four Seven

June 2018 : Puzzle

The grid is incomplete. Place numbers in some of the empty cells below so that in total the grid contains one 1, two 2’s, etc., up to seven 7’s. Furthermore, each row and column must contain exactly 4 numbers which sum to 20. Finally, the numbered cells must form a connected region*, but every 2-by-2 subsquare in the completed grid must contain at least one empty cell.

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

(*Updated 2018-06-14 to clarify that cells connect along edges only.)