Towers of Hanoi is a game with three rods and a stack of circular disks, stacked in order size as shown

in the diagram below. The goal of the game is to get all the disks over to the rightmost post from the

leftmost post in any few moves as possible. You can only move one disk at a time and you can never

stack a disk with a larger radius on top of one with a smaller one. Determine a recursive and explicit

equation for the minimum number of moves it would take to move $n$ disks to furthest rod.