  We study the Littlewood-Richardson coefficients of double Grothendieck
polynomials indexed by Grassmannian permutations. Geometrically, these are the
structure constants of the equivariant $K$-theory ring of Grassmannians.
Representing the double Grothendieck polynomials as partition functions of an
integrable vertex model, we use its Yang-Baxter equation to derive a series of
product rules for the former polynomials and their duals. The
Littlewood-Richardson coefficients that arise can all be expressed in terms of
puzzles without gashes, which generalize previous puzzles obtained by
Knutson-Tao and Vakil.
