8th Swedish Mathematical Society Problems 1968

1.  Find the maximum and minimum values of x2 + 2y2 + 3z2 for real x, y, z satisfying x2 + y2 + z2 = 1. 2.  How many different ways (up to rotation) are there of labeling the faces of a cube with the numbers 1, 2, ... , 6? 3.  Show that the sum of the squares of the sides of a quadrilateral is at least the sum of the squares of the diagonals. When