Towers of Hanoi - challenge yourself with the Hanoi strategic puzzle

Towers Of Hanoi - About

The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower and sometimes pluralized) is a mathematical game or puzzle. It consists of three rods and a number of disks of different sizes, which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.

The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:
- Only one disk can 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 smaller disk.

With 3 disks, the puzzle can be solved in 7 moves. The minimal number of moves required to solve a Tower of Hanoi puzzle is 2n − 1, where n is the number of disks.

In popular culture

In the science fiction story "Now Inhale", by Eric Frank Russell, a human is held prisoner on a planet where the local custom is to make the prisoner play a game until it is won or lost before his execution. The protagonist knows that a rescue ship might take a year or more to arrive, so he chooses to play Towers of Hanoi with 64 disks. (This story makes reference to the legend about the Buddhist monks playing the game until the end of the world.)

In the 1966 Doctor Who story The Celestial Toymaker, the eponymous villain forces the Doctor to play a ten-piece 1,023-move Tower of Hanoi game entitled The Trilogic Game with the pieces forming a pyramid shape when stacked.

In 2007, the concept of the Towers Of Hanoi problem was used in Professor Layton and the Diabolical Box in puzzles 6, 83, and 84, but the disks had been changed to pancakes. The puzzle was based around a dilemma where the chef of a restaurant had to move a pile of pancakes from one plate to the other with the basic principles of the original puzzle (i.e. three plates that the pancakes could be moved onto, not being able to put a larger pancake onto a smaller one, etc.)

In the film Rise of the Planet of the Apes (2011), this puzzle, called in the film the "Lucas Tower", is used as a test to study the intelligence of apes.

The puzzle is featured regularly in adventure and puzzle games. Since it is easy to implement, and easily recognised, it is well-suited to use as a puzzle in a larger graphical game (e.g. Star Wars: Knights of the Old Republic and Mass Effect). Some implementations use straight disks, but others disguise the puzzle in some other form. There is an arcade version by Sega/Andamiro.

A 15-disk version of the puzzle appears in the game Sunless Sea as a lock to a tomb. The player has the option to click through each move of the puzzle in order to solve it, but the game notes that it will take 32767 moves to complete. If an especially dedicated player does click through to the end of the puzzle, it is revealed completing the puzzle does not unlock the door.

In Yu-Gi-Oh! VRAINS, a hacking group called "Knight of Hanoi" create a structure named "Tower of Hanoi" within the eponymous VRAINS virtual reality network.

The problem is featured as part of a reward challenge in a 2011 episode of the American version of the Survivor TV series. Both players (Ozzy Lusth and Benjamin "Coach" Wade) struggled to understand how to solve the puzzle and are aided by their fellow tribe members.