1st Australian Mathematical Olympiad Problems 1979

1.  A graph with 10 points and 35 edges is constructed as follows. Every vertex of one pentagon is joined to every edge of another pentagon. Each edge is colored black or white, so that there are no monochrome triangles. Show that all 10 edges of the two pentagons have the same color. 2.  Two circles (not necessarily equal) intersect at A and B. A point P travels clockwise