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.

Figure 2.26
The nine squares puzzle with more states

3 5 8. 9.