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The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower and sometimes pluralized) 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 in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape. | ||
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The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules: | ||
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Only one disk can be moved at a time. | ||
Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod. | ||
No disk may be placed on top of a smaller disk. | ||
With 3 disks, the puzzle can be solved in 7 moves. The minimal number of moves required to solve a Tower of Hanoi puzzle is 2n − 1, where n is the number of disks. | ||
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An animated solution of the Tower of Hanoi puzzle for T(4, 3): | ||
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![](https://upload.wikimedia.org/wikipedia/commons/thumb/6/60/Tower_of_Hanoi_4.gif/300px-Tower_of_Hanoi_4.gif) |