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

    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 super-computer, at the University of Illinois, as late in history as 1976 to show this fact.
Other Interesting Topological Stuff...