In the first part of this series of papers, we solved LeVeque’s problem that was to establish a central limit theorem for the number of solutions of the diophantine inequality ∣∣∣∣x− pq ∣∣∣∣ ≤ f(log q) q2 in unknowns p, q with q > 0, where f is a function satisfying special assumptions and x is chosen randomly in the unit interval. In this continuation, we are interested in the almost sure beha...