A finite set of circles divides the plane into regions. Show that we can color the plane with two colors so that no two adjacent regions (with a common arc of non-zero length forming part of each region's boundary) have the same color.
Color points inside an odd number of circles blue and points inside an even number of circles red. Then we change color whenever we cross a circle.
23rd Putnam 1962
© John Scholes
5 Feb 2002