Hodge numbers of diffeomorphic complete intersections
In
Libgober, Anatoly S., Wood, John W. ``Differentiable structures on complete intersections. II." Singularities, Part 2 (Arcata, Calif., 1981), 123–133.
the authors claim that a computer search, based on their classification technique, shows that $X_3(16,10,7,7,2,2,2)$ and $X_3(14,14,5,4,4,4)$ are diffeomorphic. Unfortunately I don't know how to compute Hodge numbers, but these would seem to be good candidates.
We got four pairs of diffeomorphic complete intersections but with Hodge numbers different. Please check the link:here