Consider a variation on the nine squares puzzle. The game is the same as that described...

Consider a variation on the nine squares puzzle. The game is the same as that described in Exercise 35 except that there are three possible states for each square: white, gray, or black. The squares change as shown in Figure 2.25, but now the state changes follow the cycle white -> gray -> black -> white. Show how the winning all-black configuration can be achieved from the initial configuration shown in Figure 2.26.