Tower of Hanoi

Puzzles and mathematics have always shared a harmonious relationship. In fact, mathematical concepts are the core theme behind many of our favorites games, puzzles and riddles such as tic-tac-toe, chess, sudoku and nonograms. However, one logic problem that truly unites everyone from puzzle lovers to math geeks is the Tower of Hanoi.

The Towers of Hanoi, also called Tower of Brahma, Lucas’ Tower, or more simply, the pyramid puzzle, is a mathematical game using three rods and various numbers of colored disks stacked in descending order with the larger disk on the bottom and the smaller disks stacked on top. This creates the iconic cylinder or pyramid shape that the Tower of Hanoi is known for.

The objective of the puzzle is to arrange all the disks on a rod (on any of the 3 rods) in descending order, obeying the following rules:

• Only one disk may be moved at a time;
• Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod;
• No disk may be placed on top of a disk that is smaller than it.

*History of Tower of Hanoi*

Since the Tower of Hanoi puzzle was first introduced by French mathematician Édouard Lucas in 1883 (hence the name Lucas Tower), many myths about its origins have been shared. The most popular one is the mystical theory that it is an homage to an ancient Indian temple in Kashi Vishwanath where Brahmin priests have been acting out an ancient prophecy since the beginning of history (this is where the name Tower of Brahma came from).

This temple houses a room with three massive pillars wrapped with 64 golden disks. Acting under Brahmin rule, the priests are continually moving the disks, one disk at a time. It is believed that once the Tower of Brahma is complete, the world would end.

The Tower of Hanoi has also had a prominent role in pop culture and video games. Most notably, in a 1966 episode of Dr. Who where The Doctor was forced to play a mind-numbing 1,023-move Tower of Hanoi puzzle called “The Trilogic Game” and in the 2011 blockbuster movie Rise of the Planet of the Apes where it was used as an intelligence test for the apes.

*How to solve the Tower of Hanoi*

While the Tower of Hanoi is rooted in mathematics, you don’t need to understand or use complex math to solve it. In fact, learning how to solve it can be easier than learning card tricks!

• Recursive Solutions - Some people, particularly scientists and computer programmers, love to explore the idea of recursive solutions for Tower of Hanoi problems. At their core, recursive solutions recognize that a problem can be broken down into a collection of smaller sub-problems. Each of these sub-problems is easier to manage and the sum of their solutions combines to find the total solution for the base case. Simply put, you use the information from one step to inform the next step.

• Finding Your Own Patterns - When first presented with a Tower of Hanoi puzzle, this is the strategy most people use. You simply play the game and find your own patterns and solutions as you go. While this isn’t the most effective strategy, it’s definitely the most fun. Even if you fail, you can always just start over. That’s the fun of a game!