I believe the definition should say that is theleastnumber of moves to transfer k disks. You created some algorithm for moving disks; this shows that . This solves problem c. If you want to show that , then you also need to show that , i.e., that there does not exist a more efficient algorithm.

In fact, Wikipedia says, "Although the three-peg version has a simple recursive solution as outlined above, the optimal solution for the Tower of Hanoi problem with four pegs (called Reve's puzzle), let alone more pegs, is still an open problem."