A convex polygon is dissected into a finite number of triangles with disjoint interiors, whose sides have odd integer lengths. The triangles may have multiple vertices on the boundary of the polygon and their sides may overlap partially. Prove that the polygon's perimeter is an integer which has the same parity as the number of triangles in the dissection. Determine whether part a) holds if the polygon is not convex. Proposed by Marius Cavachi Note: the junior version only included part a), with an arbitrary triangle instead of a polygon.