  M. Kobayashi introduced a notion of duality of weight systems. We tone this
notion slightly down to a notion called coupling. We show that coupling induces
a relation between the reduced zeta functions of the monodromy operators of the
corresponding singularities generalizing an observation of K. Saito concerning
Arnold's strange duality. We show that the weight systems of the mirror
symmetric pairs of M. Reid's list of 95 families of Gorenstein K3 surfaces in
weighted projective 3-spaces are strongly coupled. This includes Arnold's
strange duality where the corresponding weight systems are strongly dual in
Kobayashi's original sense. We show that the same is true for the extension of
Arnold's strange duality found by the author and C. T. C. Wall.
