Chapter 9, Problem 2EA

In a Latin square, each treatment condition occurs first one time, second one time, third one time, and so on. Ideally, every possible sequence of two treatments should also occur exactly one time. For example, if two treatments are identified as A and B, then the sequence AB and the sequence BA should each occur one time in the square.

1. Try to construct an ideal Latin square for
an experiment with four treatment conditions identified as A, B, C, and D. This may take a little time, but it can be done.

Now, try to construct an ideal Latin square for an experiment with three treatment conditions. You should quickly find that it is impossible.