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existence of subset of points inside triangle

Source: 1998 France MO P5

April 10, 2021
geometrycombinatorics

Problem Statement

Let AA be a set of n≥3n\ge3 points in the plane, no three of which are collinear. Show that there is a set SS of 2n−52n-5 points in the plane such that, for each triangle with vertices in AA, there exists a point in SS which is strictly inside that triangle.
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