Consider the 3-Standard-Coloring. We name the colors a, b and c. If a cell is black we give it the value 1 otherwise 0. If we perform a move, notice how a,b and c are congruent to each other mod 2. If we look at the state we want to reach, namely all squares being black, we notice that two colors have the value 21, whilst the other has value 22. However this contradicts the above invariant and thus we get a contradiction. => It is impossible to color all the cells of the chessboard black.