Upon completion, the world will end…

History

The Tower of Hanoi puzzle was invented by the French mathematician Edouard Lucas in 1883. Lucas is also known for his study of the Fibonacci sequence. The related Lucas sequence is named after him. He gave a formula for finding the n th term of the Fibonacci sequence.

Lucas was educated at the Ecole Superieure. He worked in the Paris observatory and later became a professor of mathematics in Paris. In the meantime he served in the army.

What is It?

The

Tower of Hanoi

or

Towers of Hanoi

is a mathematical game or puzzle. It consists of three pegs, and a number of disks of different sizes which can slide onto any peg. The puzzle starts with the disks neatly stacked in order of size on one peg, smallest at the top, thus making a conical shape.

The objective of the game is to move the entire stack to another peg.

The Rules

•Only one disk may be moved at a time. •Each move consists of taking the upper disk from one of the pegs and sliding it onto another peg, on top of the other disks that may already be present on that peg. •No disk may be placed on top of a smaller disk.

Sound Simple???

The Solution

This illustration shows the solution to the puzzle of the Tower of Hanoi using half the number of discs for a quicker demonstration.

The Legend…

There is a legend about an Indian temple that contains a large room with three time-worn posts in it surrounded by 64 golden discs. The priests of Brahma, acting on an ancient prophecy, have been moving these discs in accordance with the rules of the puzzle. Legend has it that when the last move of the puzzle is complete, the world will end. This legend accredits the puzzles alternate name “The Tower of Brahma”. According to calculations, the process of moving all of the discs without breaking the rules of the puzzle would take 586.549 billion years. The earth is currently approximately 13.7 billion years old.

Applications

• Used in psychological research on Problem Solving • Used as Backup Rotation Scheme when performing computer data backups.

• Popular for teaching recursive algorithms to beginning programming students • Used as a memory test by neuropsychologists trying to evaluate amnesia • Used for fun in Math class after you finish a test!

“Current World” Where have

YOU

seen the Tower of Hanoi? If you have played any of these video games, you may be quite familiar with it!

Black & White The Island of Dr. Brain The Secret Island of Dr. Quandary Star Wars: Knights of the Old Republic Zork Zero The Legend of Kyrandia: Hand of Fate