Twenty Four Seven (Four-in-One)

February 2023 : Puzzle

Four Twenty Four Seven grids have been smooshified together within the 12-by-12 grid above.

Place numbers in some of the empty cells so that in total each of the four 7-by-7 outlined grids is a legal “Twenty Four Seven” grid. Namely: each 7-by-7 grid’s interior should contain one 1, two 2’s, etc., up to seven 7’s. Furthermore, each row and column within the 7-by-7’s 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.

Some numbers have been placed inside the grid. Additionally, some blue numbers have been placed outside the grid. A number outside the grid represents either the sum of the row or column it is facing, or the value of the first number it sees in that row or column.

Once completed, you can submit as your answer the product of the areas of the connected groups of orthogonally adjacent empty squares in the grid.