  We prove upper bounds on the average kissing number $k(\mathcal{P})$ and
contact number $C(\mathcal{P})$ of an arbitrary finite non-congruent sphere
packing $\mathcal{P}$, and prove an upper bound on the packing density
$\delta(\mathcal{P})$ of an arbitrary infinite non-congruent sphere packing
$\mathcal{P}$.
