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( Tower of Hanoi) The Tower of Hanoi or Towers of Hanoi (also known as The Towers of Brahma) is a mathematical game or puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks neatly stacked in order of size on one rod, the smallest at the top, thus making a conical shape.

The objective of the puzzle is to move the entire stack to another rod, obeying the following rules

The puzzle was invented by the French mathematician Édouard Lucas in 1883. There is a legend about a Vietnamese or Indian temple which contains a large room with three time-worn posts in it surrounded by 64 golden disks. The priests of Brahma, acting out the command of an ancient prophecy, have been moving these disks, in accordance with the rules of the puzzle, since that time. The puzzle is therefore also known as the Tower of Brahma puzzle. According to the legend, when the last move of the puzzle is completed, the world will end. It is not clear whether Lucas invented this legend or was inspired by it. The Tower of Hanoi is a problem often used to teach beginning programming, in particular, as an example of a simple recursive algorithm.

If the legend were true, and if the priests were able to move disks at a rate of one per second, using the smallest number of moves, it would take them 264-1 seconds or roughly 600 billion years (operation taking place is \frac{{2}^{64}-1}{60 \times 60 \times 24 \times 365.2425}) .[1] . It would take 18,446,744,073,709,551,615 turns to finish.

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