# Congratulations Mehar !!!!

Geometry Level 5

Its winter time and great mathematician Professor Nishtha has invited her batch-mates to celebrate this year's Christmas.....Prof. Nishtha decides to show off her Geometry skills to her friends and challenges her best friend , Mehar to answer the question...Her question is as follows :

Consider n disks $$C_{1}$$, $$C_{2}$$, . . . , $$C_{n}$$ in a plane such that for each $$1 \leq i < n$$, the center of $$C_{i}$$ is on the circumference of $$C_{i+1}$$, and the center of $$C_{n}$$ is on the circumference of $$C_{1}$$.

Determine the maximum possible score of such an arrangement of 24 disks to be the number of pairs $$(i, j)$$ for which $$C_{i}$$ properly contains $$C_{j}$$.