1. Consider n points on the plane such that every point is connected via edges with at least 5 other points. Show that there must always exist at least 5 closed paths (i.e. cycles) such that all of them have an even number of edges or all of them have an odd number of edges.

4. Prove that the area of an anticomplementary triangle is 4 times the area of the triangle that it is anticomplementary of. For example, Say triangle XYZ is the anticomplementary triangle of the triangle ABC. Prove that the area of triangle XYZ is 4 times the area of triangle ABC.