Example of exponential many collisions of identical hard disks in the plane

Let $\mathrm{MaxCol}(n,d)$ denote the maximal number of nonsimultaneous elastic collisions among $n$ identical hard balls moving freely in ${\mathbb{R}}^d$. We give a planar construction with exponential lower bound with respect to $n$: $\mathrm{MaxCol}(n,2)\ge 2^{\lfloor n\mathrm{/}2\rfloor },n\ge 3$.