A checkerboard is similar to a chessboard. It is also an $8\times 8$ grid of squares, just this time the colors of the squares alternate between red and black. 

For problem 2.18 we want to place two distinct checkers (red and black) on squares of the same color, on 2.19 we want the red checker on a black square and the black checker on a red square, and on 2.20 we want them to be on squares of different colors.