Applied Combinatorics Problem

4. (Liu (1972]) Suppose that we have two types of drugs to test simultaneously, such as headache remedies and fever remedies. In this situation, we might try to design an experiment in which each type of drug is tested using a Latin square design. However, we also want to make sure that, if at all possible, all combinations of headache and fever remedies are tested. For example, Table 1.9 shows two Latin square designs if we have 3 headache remedies and 3 fever remedies. Also shown in Table 1.9 is a third square, which lists as its i, j entry the i, j entries from both of the first two squares. We demand that each entry of this third square be different. This is not true in Table 1.9. (a) Find an example with 3 headache and 3 fever drugs where the combined square has the desired property