  We introduce a mutation algorithm for puzzles that is a three-direction
analogue of the classical jeu de taquin algorithm for semistandard tableaux. We
apply this algorithm to prove our conjectured puzzle formula for the
equivariant Schubert structure constants of two-step flag varieties. This
formula gives an expression for the structure constants that is positive in the
sense of Graham. Thanks to the equivariant version of the `quantum equals
classical' result, our formula specializes to a Littlewood-Richardson rule for
the equivariant quantum cohomology of Grassmannians.
