  In 1952, H. Davenport posed the problem of determining a condition on the
minimum modulus $m_{0}$ in a finite distinct covering system that would imply
that the sum of the reciprocals of the moduli in the covering system is bounded
away from $1$. In 1973, P. Erdos and J. Selfridge indicated that they believed
that $m_{0} > 4$ would suffice. We provide a proof that this is the case.
