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Found problems: 1

2013 IFYM, Sozopol, 6
Tags: ramsey number , geometry , combinatorics
Prove that for each natural number $k$ there exists a natural number $n(k)$, such that for each $m\geq n(k)$ and each set $M$ of $m$ points in the plane, there can be chosen $k$ triangles, so that each has an angle greater than $120^\circ$.