#Hanoi towers problem how to#
#Hanoi towers problem code#
#Hanoi towers problem series#

It is not clear if Lucas invented the puzzle himself or if he was inspired by the legends that shroud the source of the puzzle. But it is generally accepted that it was brought into the limelight, not only to the community of mathematicians, but also to the general public by Edouard Lucas, a French mathematician, in the year 1883. This puzzle is of unconfirmed origins, with many legends presenting different stories about where it came from. It is also known as the Tower of Brahma or the Lucas Tower. The Tower of Hanoi is one such mathematical game. Famous examples of these are the Conway’s Game of life (a cellular automaton), the Monty Hall problem (a probability puzzle, which is characteristically also similar to a veridical paradox), Bertrand’s Box problem and Fractals. These are popularly known to be a part of the branch of mathematics known as 'recreational mathematics'. There are several mathematical puzzles that have captivated, intrigued and delighted us in equal measures, over time. Only one disk can be moved at a time, and they all need to be moved to another rod, preserving the conical arrangement. The challenge lies in moving this conical arrangement to another rod.

a ring cannot be put on top of a smaller ring.Īt the start of the game, one of the rods is stacked with the rings, starting from the smallest to the biggest ring.

The goal of the game is to move all the rings to the right-most rod.

#Hanoi towers problem how to#

Move the rings to the rightmost rod by dragging them with the mouse, read below for detailed instructions on how to play and solve ths puzzle. = 2 N - 1.Tower of Hanoi (which also goes by other names like Tower of Brahma or The Lucas Tower), is a recreational mathematical puzzle that was publicized and popularized by the French mathematician Edouard Lucas in the year 1883. So, the expression for the N discs will become, Moves N = (2 * Moves N-1) + 1 = 2 N - 1. The number of moves almost doubles every time you insert another disk in the stack.

#Hanoi towers problem series#

For N = 3, the minimum number of moves required to shift from tower A to tower B is 7.Ĭan you observe some pattern or series from the above points?.For N = 2, the minimum number of moves required to shift from tower A to tower B is 3.For N = 1, the minimum number of moves required to shift from tower A to tower B is 1.We can observe the following things from the above discussion: Let us now analyze the minimum number of moves required to shift all discs from tower A to tower B.

TowerofHanoi(N - 1, inter, source, dest) Moving N - 1 discs from tower C to tower B.

Moving Nth disc from tower A to tower B.Ĭout<< ' Move disc ' << N << ' from ' << source <<' to '<< dest <<' ' TowerofHanoi(N - 1, source, dest, inter)

Moving N - 1 discs from tower A to tower C. void towerOfHanoi(int N, char source, char inter, char dest)Ĭout<< ' Move Disc 1 from ' << source << ' to ' << dest << ' '

#Hanoi towers problem code#

Now again, recursively call the function’ towerOfHanoi()’ for N – 1 discs to move them from ‘inter’ to ‘dest.’īelow is the code snippet for the same approach for your reference.

Move the Nth disc from ‘source’ to ‘dest.’.

Else recursively call the function’ towerOfHanoi()’ for N – 1 discs to move them from ‘source’ to ‘inter.’.

Design a base Case for the solution as if ‘discs’ = 1, then move it from ‘source’ to ‘dest.’.

Create a function, let’s say towerOfHanoi() with integer variable ‘N’ representing the number of discs, three-character variables, say ‘source,’ ‘dest’ and ‘inter’ representing source, destination, and intermediate positions.

Now recursively move ‘N – 1’ discs from tower C to tower B.Īfter going through the discussion on the Algorithm above, you can try to write the recursive code by following the below-mentioned steps:.

Move the ‘Nth’ disc from tower A to tower B.

Recursively, move top’ N – 1′ discs from tower A to tower C.

Now let us derive the general solution for the ‘N’ number of discs. We can see that 7 moves will be required to shift 3 Discs from tower A to tower B with the help of an intermediary tower C.