[From Thinking Mathematically, p. 11.]
Take square and draw a straight line right across it. Draw several more lines in any arrangement so that the lines all cross the square, and the square is divided into several regions. The task is to color the regions in such a way that adjacent regions are never colored the same. (Regions having only one point in common are not considered adjacent.) What is the fewest number of different colors you need to color any such arrangement?