THE TOWER OF HANOI

The Tower of Hanoi is one of the great classic puzzles. Invented by French mathematician Eduardo Lucas in 1883.

The basic problem is to move a stack of different sizes piece from one post to another: Moving one piece at a time, and never placing a larger piece on a smaller piece. Three is the minimum, and usual, number of posts.

 

The Puzzle Museum is fortunate to have one of the originals together with its instruction leaflet which is dated 1883 and refers to Lucas' book Récreations Mathématiques.

Opposite is an illustration of the box's label. It says "The game was brought from Tonkin by Professor N.Claus of Siam, Mandarin of the College of Li-Sou-Stian"

I believe that it was Gaston Tissandier, author of the wonderful 19th Century book Popular Scientific Recreations, who first disclosed the identity of the "Mandarin".

From the instruction leaflet: Claus is an anagram of Lucas and Li-Sou-Stian is an anagram of Saint Louis, the lycée where Lucas was a professor.

 

The original leaflet contained this legend:

"It is related that, in the great temple at Benares, beneath the dome which marks the centre of the world, one may see fixed in a brass-plate three diamond needles, a cubit high and as thick round as the body of a bee. On one of these needles God at the creation placed sixty-four discs of pure gold, the largest disc resting on the brass slab, and the others smaller and smaller to the top one. This is the Tower of Brahma. Night and day the priests are continually occupied in transferring the discs from the first diamond needle to the third, without infringing any of the fixed and immutable laws of Brahma. The priest must not move more than one disc at a time, he must only place this disc on an unoccupied needle, and then only on a disc larger than it. When according to these rules the sixty-four discs shall have been transferred from the needle on which the Creator placed them to the third needle, the tower and the Brahmins will all crumble into dust, and that will be the end of the world."

This story helps explain why the puzzle is sometimes called "The Tower of Brahma".

 

The Tower of Hanoi illustrates the great educational value of puzzles.

  • MATHEMATICS: Discovering the binary sequence required in solving the puzzle.
  • COSMOLOGY: Calculating when the universe would end if the legend was true.
  • GEOGRAPHY: What or Who is Annamite.
  • MATERIAL SCIENCE: Is Diamond the correct material to use for the long needles.
  • SPELLING: Anagrams.
  • HISTORY: Why was a Chinese theme used for this puzzle at that time.
  • ? : Why is the fat chap, with "AU" on his tummy, in the centre bottom of the illustration on the original lid?
 

This photograph illustrates a few of the different versions of this puzzle that have been sold commercially over the past 120 years.

 

Additional rules that can be used for more complex puzzles include:

  • 3 posts in a row. Pieces must never jump over a peg.
  • 3 posts in a triangle: Pieces can only move in a clockwise direction.
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