Problem #18

Consider a 3 x 3 checkerboard as shown in Figure 1. You are allowed to choose any 2 x 2 subsquare and rotate it 90 degrees, 180 degrees, or 270 degrees. For example, if the subsquare in the upper left hand corner is rotated 90 degrees, we obtain the pattern in Figure 2.

Can you obtain all possible patterns of 5 black squares and 4 white ones by performing sequences of operations of this type?