that the remaining 24 squares can be covered by eight 3 × 1

rectangles? If yes, find all such squares

(Hint: A domino is a 2 × 1 rectangle. As you may know,

if two diagonally opposite squares of an ordinary 8 × 8–

chessboard are removed, the remaining 62 squares cannot

be covered by 31 non-overlapping dominos. The reason

being, after removing the two corners 32 squares of one

colour and 30 of the other are left. No matter how you place

a domino it will cover one white and one black square.)

I found that if the central square is removed, the remaining squares can be covered. I don't think there are any other squares which apply.

How do you show that you cannot cover the board if you remove any other square?