| Möbius Inversion: Suppose a professor returns 100 exam papers randomly. What is the probability that at least one student receives their own exam? What is the most number of pieces you can slice a cake into using N cuts? Using N colors, how many ways are there to color the vertices of a given graph so that no edge has two vertices of the same color? These seemingly unrelated questions can all be solved using the technique of Möbius inversion. We will take a tour through a variety of situations in which Möbius inversion helps. |