Here are two new problems. Recently declassified information shows that each state is a polygon, that no more than three states meet at any point, and that, for every pair of states that share a border, there is an airport somewhere on the shared border. Given only this information, their handler, a closet mathematician, says that this mission is possible. Here if and only if . You'll just have to choose.
Some problems are just plain hard.
This course, which counts toward both mathematics and computer science majors, is concerned with the design and analysis of algorithms. I can't build bricks without clay. Along the way we'll have some fun asking and answering many questions about set theory and graph theory. For example, we'll discover the shocking fact that not all infinite sets are the same size, and we'll try to decide how many different crayons you need to color a map. In any subject in which mathematics is applied, you are likely to run into equations relating unknown functions and their derivatives.