2002 OIM Problems/Problem 2

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Problem

Given any set of 9 points in the plane of which there are not three collinear, show that for each point $P$ of the set, the number of triangles that have as vertices to three of the remaining eight points and to $P$ inside it, it is even.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe18.htm