### 23rd Putnam 1962

**Problem B4**

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.

**Solution**

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

jscholes@kalva.demon.co.uk

5 Feb 2002