From Oscar Levin's "Discrete Mathematics: An Open Introduction"

There is a monastery in Hanoi, as the legend goes, with a great hall containing three tall pillars. Resting on the first pillar are 64 giant disks (or washers), all different sizes, stacked from largest to smallest. The monks are charged with the following task: they must move the entire stack of disks to the third pillar. However, due to the size of the disks, the monks cannot move more than one at a time. Each disk must be placed on one of the pillars before the next disk is moved. And because the disks are so heavy and fragile, the monks may never place a larger disk on top of a smaller disk. When the monks finally complete their task, the world shall come to an end. Your task: figure out how long before we need to start worrying about the end of the world.

1. Do this problem for 1, 2, 3, 4, and 5 disks to find the first 5 terms in a sequence of numbers which corresponds to the minimum number of moves required.
2. Examine your sequence to find a way to recursively express it.
3. Examine your sequence to find a way to express it in closed form.
4. Use mathematical induction to prove your closed form expression.
5. If there were 64 disks and it takes a second to move a disk, how long would that take?

Use the following link to track the number of moves required:

https://www.mathplayground.com/logic_tower_of_hanoi.html