Towers of Hanoi

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]

The rec.puzzles Archive.

(2003-07-13)