This paper has been selected to receive the Gerge Axelby Oustanding Paper Award of the Control Systems Society for the biennium (1998-1999). The paper deals with the problem of deciding a mixing protocol for a prototypical mixing system. It is postulated that Entropy of a periodic sequence of transformations (which is defined in the paper as a direct generalization of the entropy of a single transformation defined in Ergodic Theory) is a good measure of mixing. Therefore, the problem is formalized as the one of finding a sequence of transformationss in a given appropriate set which has the maximum entropy. The problem is solved completely. By successively restricting the set of candidate sequences, the optimal sequence is found.