Problem #12: Dominoes on Board
A board, 9 inches by 7 inches, is marked out into 63 one-inch squares.
To make the number of squares even, the middle square is blocked out by
placing a chessman on it. John attempts to cover the board, other than
the middle square, with dominoes which are 2 inches by 1 inch.
In the figure above he has 11 dominoes in place.
Since 31 dominoes will be needed in all, more than one set will be required.
Can you completely cover the board, other than the middle square, without having
any domino stick out over the edge of the board, or can you prove it cannot be