Move the coloured discs from one peg to another with the following two contsraints:
  • You can only move one disc at a time
  • You cannot put a bigger disc on top of a smaller disc.

The minimum number of moves you will need to make to move all five discs from one peg to another is 31.


This puzzle was first published by Edouard Lucas, a French mathematician. Under the name M. Claus, he published, in 1883, the puzzle in his four volume book on recreational mathematics, Recreations mathematiques. Notice that Claus has the same letters as Lucas, Claus is an anagram of Lucas. It is thought that his use of the name "The Tower of Hanoi" was influenced by the French colonial interest in south east Asia.

In 1884 another French mathematician, De Parville, made up this story commonly associated with the puzzle.

"In the great temple at Benares, says he, beneath the dome which marks the centre of the world, rests a brass plate in which are fixed three diamond needles, each a cubit high and as thick as the body of a bee. On one of these needles, at the creation, God placed sixty-four discs of pure gold, the largest disc resting on the brass plate, and the others getting smaller and smaller up to the top one. This is the Tower of Bramah. Day and night unceasingly the priests transfer the discs from one diamond needle to another according to the fixed and immutable laws of Bramah, which require that the priest on duty must not move more than one disc at a time and that he must place this disc on a needle so that there is no smaller disc below it. When the sixty-four discs shall have been thus transferred from the needle on which at the creation God placed them to one of the other needles, tower, temple, and Bramahns alike will crumble into dust, and with a thunderclap the world will vanish."

W W R Ball, Mathematical Recreations and Essays, page 304

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