Thus, after placing all 31 dominoes: Covered black squares = 31, covered white squares = 31.
But we have 30 black and 32 white available → because we would need to cover 31 black squares but only 30 exist. 8.1.6 Complete Chessboard
→ total black covered = total white covered = number of dominoes. Thus, after placing all 31 dominoes: Covered black