Question 24
A chain of $n$ identical circles $C_1,C_2,\ldots,C_n$ of equal radii and centres on the $x$-axis lie inside the ellipse $E:\dfrac{x^2}{2023}+\dfrac{y^2}{333}=1$ such that $C_1$ is tangent to $E$ internally at $(-\sqrt{2023},0)$, $C_n$ is tangent to $E$ internally at $(\sqrt{2023},0)$, and $C_i$ is tangent to $C_{i+1}$ externally for $i=1,\ldots,n-1$. Determine the smallest value of $n$.