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diagonals in a convex 2014-gon

Source: 2015 Latvia BW TST P4

December 16, 2022
geometrydiagonalscombinatorial geometry

Problem Statement

Can you draw some diagonals in a convex 20142014-gon so that they do not intersect, the whole 20142014-gon is divided into triangles and each vertex belongs to an odd number of these triangles?