  We generalize our puzzle formula for ordinary Schubert calculus on
Grassmannians, to a formula for the T-equivariant Schubert calculus. The
structure constants to be calculated are polynomials in {y_{i+1} - y_i}; they
were shown (abstractly) to have positive coefficients in [Graham]
math.AG/9908172. Our formula is the first to be manifestly positive in this
sense. In particular this gives a new and self-contained proof of the ordinary
puzzle formula, by an induction backwards from the "most equivariant" case.
  The proof of the formula is mostly combinatorial, but requires no prior
combinatorics, and only a modicum of equivariant cohomology (which we include).
  This formula is closely related to the one in [Molev-Sagan] q-alg/9707028 for
multiplying factorial Schur functions in three sets of variables, although
their rule does not give a positive formula in the sense of [Graham]. We
include a cohomological interpretation of this problem, and a puzzle
formulation for it.
