At the same time, I suggested that certainty was an ideal, even if it was never attained, in the arts. I will talk about some related ideas on Wednesday that do have parallels in art.
Every domino covers a square of each color.
31 dominoes would cover 31 white squares and 31 black squares. But the mutilated board is missing two squares of the same color so the number of black squares doesn't equal the number of white squares. By the way, this is a good example of mathematical certainty. If you try and try and try and try to cover the checkerboard and fail, you may be pretty sure it can't be done, but you aren't certain . The argument above, however, gives you certainty that it can't be done.