22nd Eötvös Competition Problems 1915

1.  Given any reals A, B, C, show that An2 + Bn + C < n! for all sufficiently large integers n. 2.  A triangle lies entirely inside a polygon. Show that its perimeter does not exceed the perimeter of the polygon. 3.  Show that a triangle inscribed in a parallelogram has area at most half that of the parallelogram. SolutionsProblem 1Given any reals A, B, C, show