The document describes the Tower of Hanoi puzzle. The objective is to move a stack of disks from the starting tower to the goal tower using a third tower, obeying the rules that only one disk can be moved at a time and a larger disk can never be placed on top of a smaller disk. An algorithm for solving the puzzle recursively is presented. The Tower of Hanoi is used in research, computer backups, teaching recursion, and testing frontal lobe functions.

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SUBMITTED BY:-
NAME:- MD. HALIM
CLASS ROLL:- L18/CS/154
UNIVERSITY ROLL:- 10300118015
SUBJECT:- DESIGN & ANALYSIS OF
ALGOTITHM (CS501)
Haldia Institute Of Technology
ICARE Complex HIT, Haldia (WB)
Tower of Hanoi Method

2. Introduction
The Tower of Hanoi was invented by the French mathematician
Edouard Lucas and sold as a toy in 1883. It originally bore the name
of ”Prof.Claus” of the college of “LiSou Stain”, but these were soon
discovered to be anagrams for “Prof.Lucas” of the college of “Saint
Loius”, the university where he worked in Paris.
There is a history 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 the Brahma, since
that time. According to the legend, when the last move of the puzzle will be
completed, the world will end.

3. Objective
The aim of the tower of Hanoi problem is to move the initial n different
sized disks from Tower A to Tower C using a temporary Tower B. The rule is
that no larger disk is to be placed above the smaller disk in any of the
needle while moving or at any time, and only the top of the disk is to be
moved at a time from any Tower to any Tower.

4. Rules of Puzzle
The Tower of Hanoi 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. The objective of the puzzle is to move the entire stack to
another rod, obeying the following rules:
 Only one disk must be moved at a time.
 Each move consists of taking the upper disk from one of the rods and sliding it onto
another rod, on top of the other disks that may already be present on that rod.
 No disk may be placed on top of a smaller disk.

5. Algorithm
Input :- Input of discs in Tower of Hanoi , specification of ORG as
from the piller and DES as to piller,INT as the intemediate piller.
Output :- Steps of moves of N discs from piller ORG to DCS
piller.
Steps 1. if N>0 then
2. move(N-1 ,ORG ,DES ,INT)
3. ORG DES (move from ORG to DES)
4. move(N-1 ,INT ,ORG ,DES)
5. end if
6. stop

6. Applications
The Tower of Hanoi is frequently used in psychological research on problem solving.
There also exists a variant of this task called Tower of London for neuropsychological
diagnosis and treatment of executive functions.
 The Tower of Hanoi is also used as a Backup rotation scheme when performing
computer data Backups where multiple tapes/media are involved.
 As mentioned above, the Tower of Hanoi is popular for teaching recursive
algorithms to beginning programming students. A pictorial version of this puzzle is
programmed into the emacs editor, accessed by typing M-x hanoi. There is also a
sample algorithm written in Prolog.
 The Tower of Hanoi is also used as a test by neuropsychologists trying to evaluate
frontal lobe deficits.

7. Conclusion

8. Reference
 Hofstadter, Douglas R. (1985). Metamagical Themas : Questing for the Essence of Mind and
Pattern. New York: Basic Books. ISBN 978-0-465-04540-2.
 Hinz, Andreas M.; Klavžar, Sandi; Milutinović, Uroš; Petr, Ciril (2013-01-31). The Tower of Hanoi –
Myths and Maths. ISBN 978-3034802369.
 Spitznagel, Edward L. (1971). Selected topics in mathematics. Holt, Rinehart and Winston.
p. 137. ISBN 978-0-03-084693-9.
 Moscovich, Ivan (2001). 1000 playthinks: puzzles, paradoxes, illusions & games.
Workman. ISBN 978-0-7611-1826-8.
 Petković, Miodrag (2009). Famous Puzzles of Great Mathematicians. AMS Bookstore.
p. 197. ISBN 978-0-8218-4814-2.
 Troshkin, M. "Doomsday Comes: A Nonrecursive Analysis of the Recursive Towers-of-Hanoi
Problem". Focus (in Russian). 95 (2): 10–14.