3

Part of 2007 APMO

Problems(1)

$n$ disks in a plane

Source: APMO 2007

n

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}

. Define the score of such an arrangement of

n

disks to be the number of pairs

(i; j )

C_{i}

properly contains

C_{j}

. Determine the maximum possible score.

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