IMO Shortlist 2015 problem G8
A triangulation of a convex polygon is a partitioning of 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 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.)