Question 16
Consider a $ 2025 \times 2025 $ grid of unit squares. We place on the grid some number of rectangular tiles, possibly of different sizes, such that each side of every tile lies on a grid line and every unit square is covered by at most one tile.
Determine the minimum number of tiles we need to place so that each row and each column has exactly one unit square that is not covered by any tile.
Determine the minimum number of tiles we need to place so that each row and each column has exactly one unit square that is not covered by any tile.