The constraints are that only one ring can be moved from one peg to the other in one move, and a larger ring cannot be placed on top of a smaller ring. The task is to move this column on rings from the Source peg to the Destination peg using the Temp peg as temporary storage of the rings.

There are n concentric rings of different sizes on the Source peg in such a way that the bottom most ring is the largest and the topmost ring is the smallest and a larger ring is not placed on a smaller ring. There are three pegs Source, Temp, Destination. In this post I will describe the basic recursive solution to the Towers of Hanoi It is not clear whether Lucas invented this legend or was inspired by it. According to the legend, when the last move of the puzzle is completed, the world will end.

The puzzle is therefore also known as the Tower of Brahma puzzle. Brahmin priests, acting out the command of an ancient prophecy, have been moving these disks, in accordance with the rules of the puzzle, since that time. There is a legend about an Indian temple which contains a large room with three time-worn posts in it surrounded by 64 golden disks. The puzzle was invented by the French mathematician Г‰douard Lucas in 1883. The constraints are we can move only one disk at a time, and we may use the third peg as a temporary storage for the disks, and a larger disk cannot be placed on top of a smaller disk. The task is to transfer such a column of disks from a source peg to another destination peg. Towers of Hanoi is a mathematical game or a puzzle in which there are three pegs, and some disks (originally 8) of different radius placed on top of one another such that no larger disk is placed on a smaller disk.

Recureence tree hanoi towers