In the diagram, the two circled squares are removed. Their horizontal and vertical distance are x, y. It is obvious that x+y= odd number. Let's assume x is even and y is odd. If not, simply turn the board by 90 degrees.
in the rectangle formed by the two removed squares, covering the rectangle is easy, as indicated in the diagram. Out side of the rectangle, divide the board into several areas. Obviously, column A,B,G,H are all 1x8 rectangles, so they can be covered. As for column C,D,E,F, the two rectangles both have their horizontal edge being X, which is even, so the two rectangles are also covered.
