Prove that an 8 x 8 chessboard can be completely covered using dominos ( 1 x 2 pieces )!?

Question

exercises from methods of proving theorems

Answer 1

Just break the chessboard into eight 8x1 rectangles. Clearly, 4 dominoes can be placed in each rectangle.

For a more interesting problem: if two opposite corners of the 8x8 chessboard are eliminated, the remaining 62 squares can NOT be completely covered using 31 dominoes.

Answer 2

Two dominoes can be arranged into a 2 x 2 square.
The chessboard can be subdivided into 4 x 4 such squares.

(The fact that the size of the dominoes is a divisor of the size of the chessboard is not sufficient.)