Since no one answered my previous questions about the inaccurate truth tellers and liars, I'l try something new:

Imagine that you have a chessboard (a black and white 8x8 board) and a set of 32 domino pieces. It's easy to see how the 32 dominos can cover the whole chessboard.
Now imagine that I broke off 2 squares from the diagonals of the chessboard (as in the attached illustration). Can I fully cover it with 31 dominos?