6th Iberoamerican Mathematical Olympiad Problems 1991

A1.  The number 1 or the number -1 is assigned to each vertex of a cube. Then each face is given the product of its four vertices. What are the possible totals for the resulting 14 numbers? A2.  Two perpendicular lines divide a square into four parts, three of which have area 1. Show that the fourth part also has area 1. A3.  f is a function defined on all