Question 3
Consider $n$ disks $C_1,C_2,\ldots,C_n$ in a plane such that for each $1\le i\lt n$, the centre of $C_i$ is on the circumference of $C_{i+1}$, and the centre of $C_n$ is on the circumference of $C_1$. Define the score to be the number of pairs $(i,j)$ for which $C_i$ properly contains $C_j$. Determine the maximum possible score.
