Problem

You are given a set of three towers, each of which has a number of disks of different sizes. Your goal is to move all the disks from the first tower to the third tower, such that each disk is on top of a larger disk. You can only move one disk at a time, and you can only move a disk to the top of another tower if that tower has no disks on it, or if the top disk on that tower is larger than the disk you are trying to move.
Example input:
3
2
1
Example output:
1
2
3

Solution

# The optimal solution is to move the smallest disk to the middle tower, then the next smallest disk to the third tower, then the smallest disk to the third tower, then the next smallest disk to the middle tower, then the smallest disk to the first tower, then the next smallest disk to the third tower, then the smallest disk to the third tower.
# This solution is optimal because it is the only solution that moves the smallest disk the least amount of times.