AnotherExercise
Another problem type that relates to topology
is seen in a classic mathematical problem known as the 4color problem.
The directions for this exercise are as follows:

Print out the map on this page.

Color it so that no two bordering states have the same color.
Try using only four colors.
Map makers have known for years that four
colors will suffice for this type of problem. In order to prove this
theorem, it took mathematicians, and a supercomputer, at the University
of Illinois, as late in history as 1976 to show this fact.