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 \(C_{j}\).

Mehar answers the Maximum score correctly. What is her answer? .

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