Answer
20 paperclips
Work Step by Step
We know that the balloon will lose its buoyancy when the force of gravity exceeds the force of the buoyancy of the balloon. Thus, we find:
$\frac{4}{3}\pi(.14^3)(.18)g+.0016g +(6.3\times10^{-4})(n)g=\frac{4}{3}\pi(.14^3)(1.29)g \\ n =20$
