I am attending a course on combinatorics. I was asked to present Möbius functions on lattices for this course. I was trying to look for a simple non-trivial problem that illustrates the need for lattice theory. All the standard texts define posets, lattices and get into proving theorems about different lattices and their ideal structures and so on. However I could'nt find a simple problem that was illuminating when viewed from the lattice viewpoint.
Other than the standard application of Möbius functions to divisors and cardinalities of sets, is there a simple problem (a puzzle would be even better!) that I can use to motivate Möbius functions on lattices?