2021 OIM Problems/Problem 6

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Problem

Consider a regular polygon with $n$ sides, $n \ge 4$, and let $V$ be a subset of $r$ vertices of the polygon. Show that if $r(r - 3) \ge n$, then there exist at least two congruent triangles whose vertices are in $V$.

Solution

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See also

https://olcoma.ac.cr/internacional/oim-2021/examenes