Double Trouble

Logic Level 3

Suppose there is/are \(n\) points on the circumference of the circle, define \(f(n) \) as the number of pieces for which a circle is divided with these points are joined by chords such that no more than 2 chords intersect at the same point.

The diagram above shows that \(f(1) = 1, f(2) =2, f(3) =4\), \(f(4) = 8, f(5) = 16 \). Find the value of \(f(6) \).

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