We classify, up to some lattice-theoretic equivalence, all possible configurations of rational double points that can appear on a surface whose minimal resolution is complex Enriques surface.

We prove an estimate on the number of rational points Grassmannian variety bounded twisted height, refining classical results Schmidt (Duke Math J 35:327–339, 1968) and Thunder (Compos 88(2):155–186, 1993) over field: most importantly, our formula counts all points. Among consequences are a couple new implications subject counting flag varieties.