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Tower Of Hanoi

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Tower Of Hanoi

This puzzle was created by Édouard Lucas in 1883. The following text is a translation by W. W. Rouse Ball of a story about the origin of the puzzle by Henri de Parville:

In the great temple at Benares, 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 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 thunder-clap the world will vanish.

Interestingly the priests will require 264 - 1 moves to complete the task, which, at one disc per second would take:
   18,446,744,073,709,551,615 seconds (nearly 585 billion years)!

Your task is a little easier, as you can select between 2 and 8 discs (which would take the priests anywhere between 3 and 255 seconds).

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