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Point always lies inside triangle

Source: Kvant Magazine No. 8 2021 M2664

March 9, 2023

combinatorial geometryKvantcombinatorics

Problem Statement

The point

O{}

is given in the plane. Find all natural numbers

n{}

for which

n{}

points in the plane can be colored red, so that for any two red points

A{}

and

B{}

there is a third red point

C{}

is such that

O{}

lies strictly inside the triangle

ABC

.
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