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diagonals in convex n-gon

Source: Polish MO Finals 1974 p6

August 23, 2024
geometrypolygoncombinatorial geometry

Problem Statement

Several diagonals in a convex nn-gon are drawn so as to divide the nn-gon into triangles and:
(i) the number of diagonals drawn at each vertex is even; (ii) no two of the diagonals have a common interior point.
Prove that nn is divisible by 33.
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