Donuts of Hanoi

The Donuts of Hanoi is a mathematical game or puzzle (based on Tower of Hanoi) consisting of three rods and a number of donuts of various diameters, which can slide onto any rod. The puzzle begins with the donuts stacked on one rod in order of decreasing size, the smallest at the top, thus approximating a conical shape. The objective of the puzzle is to move the entire stack of donuts to one of the other rods, obeying the following rules:Only one donut may be moved at a time.Each move consists of taking the upper donut from one of the stacks and placing it on top of another stack or on an empty rod.No donut may be placed on top of a donut that is smaller than it.