Tile and Trouble

May 2014 : Puzzle

Add square tiles to the 12-by-12 grid so that the total points in each row and each column matches the corresponding value outside the grid.

  • A tile can have any side length (e.g., 1-by-1, 2-by-2, 3-by-3, etc.)
  • Every cell within an n-by-n tile is worth n points.
  • Tiles may not overlap. Not every cell in the 12-by-12 grid needs to be inside one of the tiles.
  • For your answer, submit the product of the areas of each contiguous empty space in the solved grid.