  The landscape of string vacua is very large, but generally expected to be
finite in size. Enumerating the number and properties of the vacua is an
important task for both the landscape and the swampland, in part to gain a
deeper understanding of what is possible and "generic". We obtain an exact
counting of distinct intersecting brane vacua of type IIA string theory on the
$\mathbb{T}^6/\mathbb{Z}_2\times\mathbb{Z}_2$ orientifold. Care is taken to
only count gauge-inequivalent brane configurations. Leveraging the recursive
nature by which branes may be added together one-by-one, we use dynamic
programming to efficiently count the number of solutions of the tadpole,
K-theory and supersymmetry consistency conditions. The distributions of 4D
gauge group rank and complex structure moduli for the entire ensemble of
intersecting brane vacua are presented. The methods we developed here may be
useful in obtaining sharp upper and lower bounds on other corners of the
landscape.
