Where to place x_i's?

Discrete Mathematics Level 5

Let \(A\) be a convex \(61-\)gon. We then place \(n\) points \(\{x_i\}_{i=1}^n \) in the interior of \(A\). What is the minimum number \(n\), such that the interior of any triangle, whose vertices are also vertices of \(A\), will contain at least one of the points \(x_i\)?

Details and assumptions

We are free to choose where to place the points \(x_i\).

The interior of the polygon does not include the edges of the polygon. The edges of the polygon are known as the boundary of the polygon. It separates the interior from the exterior.


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