  We study statistical properties of an NP-complete problem, the subset sum,
using the methods and concepts of statistical mechanics. The problem is a
generalization of the number partitioning problem, which is also an NP-complete
problem and has been studied in the physics literature. The asymptotic
expressions for the number of solutions are obtained. These results applied to
the number partitioning problem as a special case are compared with those which
were previously obtained by a different method. We discuss the limit of
applicability of the techniques of statistical mechanics to the present
problem.
