Question 8
Let $D_{1}, \ldots, D_{n}$ be closed discs in the plane. (A closed disc is the region limited by a circle, taken jointly with this circle.) Suppose that every point in the plane is contained in at most 2003 discs $D_{i}$. Prove that there exists a disc $D_{k}$ which intersects at most $7\cdot2003-1$ other discs $D_{i}$.