TOWER OF HANOI
In 1883 the french mathematician Édouard Lucas, the number theory scholar who became famous for "the analysis on the Fibonacci sequence"(1) and creator of countless games and puzzles, invented the Tower of Hanoi game. To draw more attention to this game he invented the ancient Indian legend of the Tower of Hanoi.
The legend tells that in the Temple of Brahma in Benares(2), under a dome that represents the center of the world, is located a brass plate on which are placed 64 golden disk threaded on a needle. Monks move one at a time disks on another needle according to the rule that a large disk can never be put on a smaller disk.
In 1883 the french mathematician Édouard Lucas, the number theory scholar who became famous for "the analysis on the Fibonacci sequence"(1) and creator of countless games and puzzles, invented the Tower of Hanoi game. To draw more attention to this game he invented the ancient Indian legend of the Tower of Hanoi.
The legend tells that in the Temple of Brahma in Benares(2), under a dome that represents the center of the world, is located a brass plate on which are placed 64 golden disk threaded on a needle. Monks move one at a time disks on another needle according to the rule that a large disk can never be put on a smaller disk.
When all disks are moved, recreating a Tower on another needle, then comes the end of the world.
Often, in internet this legend is considered incorrectly real, taking away the merits from the mathematician Édouard Lucas.
I remembered it only as a curiosity.
The computer game consists of three needles, but only on one of them are threaded some disks of different sizes (down the largest and at the top the smallest).
The game has only two rules:
Often, in internet this legend is considered incorrectly real, taking away the merits from the mathematician Édouard Lucas.
I remembered it only as a curiosity.
The computer game consists of three needles, but only on one of them are threaded some disks of different sizes (down the largest and at the top the smallest).
The game has only two rules:
1) to move only the disk located on the top of a Tower
2) never put a larger disk on another smaller
2) never put a larger disk on another smaller
The aim of the game is to place (by moving them) all disks on other needle so that they are always located in the same order.
Mathematically it appens that: If the disks are n then the minimum number of moves to complete the game consists of 2n - 1.
Theoretically the game could be done with a larger number of disks, but the player should have a long free time; if to move "only" 32 disks are needed 232 - 1 moves, that is 9.223.372.036.854.775.807 moves and imagining perform a move to the second... I leave you to calculate how many years are necessary to complete this super game.
Mathematically it appens that: If the disks are n then the minimum number of moves to complete the game consists of 2n - 1.
Theoretically the game could be done with a larger number of disks, but the player should have a long free time; if to move "only" 32 disks are needed 232 - 1 moves, that is 9.223.372.036.854.775.807 moves and imagining perform a move to the second... I leave you to calculate how many years are necessary to complete this super game.
Édouard Lucas (1842-1891)
1) The succession or numerical sequence takes its name from Leonardo Fibonacci the Pisan mathematician of the 13th century.
2) Benares, today named Varanasi, is considered cultural capital of India and the holy city of Hindus; it is located on the Ganges banks and has the characteristic of being the oldest living city in the world with its 3000 years of history.
2) Benares, today named Varanasi, is considered cultural capital of India and the holy city of Hindus; it is located on the Ganges banks and has the characteristic of being the oldest living city in the world with its 3000 years of history.