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Difference between revisions of "2024 USAMO Problems/Problem 3"

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Latest revision as of 22:32, 20 March 2024

Let $m$ be a positive integer. A triangulation of a polygon is $m$-balanced if its triangles can be colored with $m$ colors in such a way that the sum of the areas of all triangles of the same color is the same for each of the $m$ colors. Find all positive integers $n$ for which there exists an $m$-balanced triangulation of a regular $n$-gon. Note: A triangulation of a convex polygon $\mathcal{P}$ with $n \geq 3$ sides is any partitioning of $\mathcal{P}$ into $n-2$ triangles by $n-3$ diagonals of $\mathcal{P}$ that do not intersect in the polygon's interior.

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