THE CHESS BOARD
We all know that a chess board has 64 squares. This can be completely covered by 32 cardboard rectangles, each cardboard covering just 2 squares.* Supposing we remove 2 squares of the chess board at diagonally opposite corners, can we cover the modified board with 31 rectangles? If it can be done how can we do it? And if it cannot be done, prove it impossible.