Tower Of Hanoi game

is a mathematical game based on the powers of 2 who purpose to move all the disks to the last pole to reconstruct tower exactly as it was before. The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower and sometimes pluralized as Towers) 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.

Rating:

100% (5 reviews)

Game controls:

Use your mouse

Tips:

there are 3 poles. In the first of them there are some disks with different dimensions, ordered from largest to smallest one. You must move a disk at once, but keep in mind that a greater disk cannot be placed over a smaller one. At left you can choose the difficulty level, the number of disks you want to use ( 1 to 8).
Tower Of Hanoi game

Iterative solution

Animation of an iterative algorithm solving 6-disk problem A simple solution for the toy puzzle is to alternate moves between the smallest piece and a non-smallest piece. When moving the smallest piece, always move it to the next position in the same direction (to the right if the starting number of pieces is even, to the left if the starting number of pieces is odd). If there is no tower position in the chosen direction, move the piece to the opposite end, but then continue to move in the correct direction. For example, if you started with three pieces, you would move the smallest piece to the opposite end, then continue in the left direction after that. When the turn is to move the non-smallest piece, there is only one legal move. Doing this will complete the puzzle in the fewest moves.

Pictures

Solution for 4 disks

Solution for 5 disks

Solution for 6 disks

Video with solution for 8 disks

Reviews

Brad, Austin, TX, US
The puzzle was invented by the French mathematician Édouard Lucas in 1883. Numerous myths regarding the ancient and mystical nature of the puzzle popped up almost immediately. These myths are recounted in the monograph The Tower of Hanoi—Myths and Maths.

Benjamin, Tulsa, OK, US
There is a story about an Indian temple in Kashi Vishwanath which contains a large room with three time-worn posts in it, surrounded by 64 golden disks. Brahmin priests, acting out the command of an ancient prophecy, have been moving these disks in accordance with the immutable rules of Brahma since that time.

Cornel, Constanta, CT, Romania
According to the legend, when the last move of the puzzle is completed, the world will end. 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 585 billion years to finish, which is about 42 times the current age of the Universe.

James, Saint Paul, MN, US
Nice graphics! Tower Of HanoiThis is precisely the nth Mersenne number! First, I had difficulties. But after several attempts, everything went very well.

Simpler statement solution

For an even number of disks:
make the legal move between pegs A and B (in either direction),
make the legal move between pegs A and C (in either direction),
make the legal move between pegs B and C (in either direction),
repeat until complete.
For an odd number of disks:
make the legal move between pegs A and C (in either direction),
make the legal move between pegs A and B (in either direction),
make the legal move between pegs B and C (in either direction),
repeat until complete.
In each case, a total of 2n − 1 moves are made.