I do not know how to start with the following exercise:
Fix $x \in \mathbb{Z}_n$ and randomly (u.i.d.) chosse $r_1,r_2,\ldots,r_q \in \mathbb{Z}_n$. Show that when $q$ is chosen as $q = \lfloor \sqrt{2n} \rfloor$ the probability $p$ that there exists $i$ and $j$ such that $r_i = x + r_j \bmod n$ is at least $p = 0.6$.
Could you give me a hint on how to start with this exercise?