Let us return to our problem from the intelligence test to see how generate and test might apply as a problem solving method. Again, here is a problem that we encountered earlier. Notice that this is a more complicated problem than the guards and prisoners problem. Here is why. In case of the guards and prisoner problem, each transformation from one state to another, was a discrete transformation. One could take a certain number of guards to the other side. One could take a certain number of prisoners to the other side, or one could take a certain of number of guards and prisoners to the other side. In this case, if I look at the approximation between A and B, and I notice that the diamond inside the circle is now outside the circle and is larger. Now suppose I were to try the same transformation from C to D. So I can look at the circle inside the triangle, put it outside, and also make it larger. I notice that when I put it outside, I can put it outside right next to the triangle, a little bit farther, a little bit farther, a little bit farther away. I can make it the same size, or a little larger, or a lot larger. Increase its size by 50% or 51% or 52%. So this space of possibilities here is very large. So for problems of this kind, the need for a smarter generator and a smarter tester is critical, because this space of possibilities can become very large, very quickly.