IMO Shortlist 2015 problem G8

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Dodao/la: arhiva
30. kolovoza 2018.

A triangulation of a convex polygon \Pi is a partitioning of \Pi into triangles by diagonals having no common points other than the vertices of the polygon. We say that a triangulation is a Thaiangulation if all triangles in it have the same area.

Prove that any two different Thaiangulations of a convex polygon \Pi differ by exactly two triangles. (In other words, prove that it is possible to replace one pair of triangles in the first Thaiangulation with a different pair of triangles so as to obtain the second Thaiangulation.)