Introduction. Let (Q,o) be a quasigroup of order n and define an n2 × 3 array A by (x,y,z) is a row of A if and only if x o y = z. As a consequence of the fact that the equations a o x = b and y o a = b are uniquely solvable for all a,b ε Q, if we run our fingers down any two columns of A we get each ordered pair belonging to Q × Q e×actly once. An n2 × 3 array with this property is called an orthogonal array and it doesn't take the wisdom of a saint to see that this construction can be reversed. That is, if A is any n2 × 3 orthogonal array (defined on a set Q) and we define a binary operation o on Q by x o y = z if and only if (x,y,z) is a row of A, then (Q,o) is a quasigroup. Hence we can think of a quasigroup as an n2 × 3 orthogonal array and conversely. Now given an n2 × 3 orthogonal array A there is the irresistable urge to permute the columns of A. One of the reasons for this urge is that the resulting n2 × 3 array is still an orthogonal array. (If running our fingers down any two columns of A gives every ordered pair of Q × Q exactly once, the same must be true (of course) if we rearrange the columns.)