We shall briefly outline the history of Latin squares and
orthogonality and their applications in experimental design.
There cannot be a pair of orthogonal Latin squares of order
6; this means that certain experimental design problems are
insoluble. We shall discuss two techniques - one related to
a recent puzzle, the 36Cube Puzzle, and the other to a
generalization of Sudoku - that lead to statistically useful types of design.
Biography: Walter Wallis graduated from the University of Sydney in 1963 and received his Ph.D. from there in 1967. He has taught at La Trobe University and the University of Newcastle in Australia and at Southern Illinois University, Carbondale, where he is now an Emeritus Professor. He has written about 300 papers and a number of books. His research finterests include Combinatorial Designs, Latin Squares, One-Factorizations and Graph Labelings.