Clue to Puzzle #16: Covering a Chess Board With Dominoes

16. You have a chessboard (8x8) plus a big box of dominoes (each 2x1). I use a marker pen to put an "X" in the squares at coordinates (1, 1) and (8, 8) - a pair of diagonally opposing corners. Is it possible to cover the remaining 62 squares using the dominoes without any of them sticking out over the edge of the board and without any of them overlapping? You cannot let the dominoes stand on their ends

picture of a chessboard

Do you notice anything about the squares at 1,1 and 8,8?

Anything that they have in common?

Where next?
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