Next, let’s symbolize the conditions. The gray cat and the tabby cat are in different cages can be summarized as: **If G, ^T or if T, ^G.**

We can also write this as **G ? T**.

The second condition tells us that the black cat is in cage three only if the white cat is also in cage three. We can write this as: **3: if B, then W**

The next condition tells us that each cage contains a different number of cats. This can be represented as **1 ? 2 ? 3**

We are told that the orange cat is in cage 2. This is simply represented as: **2: O**

Finally, we are told that there is at least one cat in each cage. We can write this as: **1, 2, 3 ? 0**

What else does this statement tell us? Well, if there are three cages, each containing one cat, and we have seven cats all together, then the maximum possible number of cats in any one cage would be five. (Since one cat would be in each of the other cages.)

Let’s draw a diagram to help us think about the problem.