# Towers of Hanoi

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<games> A classic computer science problem, invented by Edouard Lucas in 1883, often used as an example of recursion.

"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 Brahmins alike will crumble into dust, and with a thunderclap the world will vanish."

The recursive solution is: Solve for n-1 discs recursively, then move the remaining largest disc to the free needle.

Note that there is also a non-recursive solution: On odd-numbered moves, move the smallest sized disk clockwise. On even-numbered moves, make the single other move which is possible.

["Mathematical Recreations and Essays", W W R Ball, p. 304]

(2003-07-13)

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