  Within the replica framework we study analytically the instance space of the
number partitioning problem. This classic integer programming problem consists
of partitioning a sequence of N positive real numbers $\{a_1, a_2,..., a_N}$
(the instance) into two sets such that the absolute value of the difference of
the sums of $a_j$ over the two sets is minimized. We show that there is an
upper bound $\alpha_c N$ to the number of perfect partitions (i.e. partitions
for which that difference is zero) and characterize the statistical properties
of the instances for which those partitions exist. In particular, in the case
that the two sets have the same cardinality (balanced partitions) we find
$\alpha_c=1/2$. Moreover, we show that the disordered model resulting from hte
instance space approach can be viewed as a model of replicators where the
random interactions are given by the Hebb rule.
