  Given $n$ positive integers $a_1,a_2,\dots,a_n$, and a positive integer right
hand side $\beta$, we consider the feasibility version of the subset sum
problem which is the problem of determining whether a subset of
$a_1,a_2,\dots,a_n$ adds up to $\beta$. We show that if the right hand side
$\beta$ is chosen as $\lfloor r\sum_{j=1}^n a_j \rfloor$ for a constant $0 < r
< 1$ and if the $a_j$'s are independentand identically distributed from a
discrete uniform distribution taking values ${1,2,\dots,\lfloor 10^{n/2}
\rfloor }$, then the probability that the instance of the subset sum problem
generated requires the creation of an exponential number of branch-and-bound
nodes when one branches on the individual variables in any order goes to $1$ as
$n$ goes to infinity.
