Where to place x_i's?

Probability Level 5

Let AA be a convex 6161-gon. We then place nn points {xi}i=1n\{x_i\}_{i=1}^n in the interior of AA. What is the minimum number nn, such that the interior of any triangle, whose vertices are also vertices of AA, will contain at least one of the points xix_i?

Details and assumptions

We are free to choose where to place the points xix_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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