39th Eötvös Competition Problems 1935

1.  x1, x2, ... , xn is any sequence of positive reals and yi is any permutation of xi. Show that ∑ xi/yi ≥ n. 2.  S is a finite set of points in the plane. Show that there is at most one point P in the plane such that if A is any point of S, then there is a point A' in S with P the midpoint of AA'.