Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Induction III"
Read Section 3.2. The reading presents a proof that an initial configuration of the 9-number puzzle cannot be transformed into its inverse. The proof uses the fact that after each move the number of inversions remains even; this is an invariant. Invariants are used in proofs and in proving the correctness of programs.
Invariants are only introduced in this course; they are covered in detail in programming language courses.