Recursive Tower of Hanoi with(GUI)

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Introduction

According to the legend of the Tower of Hanoi (originally the "Tower of Brahma" in a temple in the Indian city of Benares), the temple priests are to transfer a tower consisting of 64 fragile disks of gold from one part of the temple to another, one disk at a time. The disks are arranged in order, no two of them the same size, with the largest on the bottom and the smallest on top. Because of their fragility, a larger disk may never be placed on a smaller one, and there is only one intermediate location where disks can be temporarily placed. It is said that before the priests complete their task the temple will crumble into dust and the world will vanish in a clap of thunder.

Does this make mathematical sense?

In the classic math problem, there are three posts. Disks of different sizes (call the number of disks "n") are placed on the lefthand post, arranged by size with the smallest on top. You are to transfer all the disks to the righthand post in the fewest possible moves, without ever placing a larger disk on a smaller one. One move is considered to be moving one disk from one post to another post.