HW1: Given a finite set of points X in the plane with diameter 1 (the distance between any two points is atmost 1), there exists a circle of radius 1/sqrt(3) containing all the points in X.
a) Prove the statement when there are exactly 3 points in X
b) Prove it for a general finite set X
Hw2: Consider a complete graph on the real numbers as vertices. Show that there exists a coloring of its edges with the natural numbers (every color is an integer) such that there does not exist a monochromatic K_3 (clique of three vertices).