Study of the tower of Hanoi problem and its generalization

Document Type : Research Paper

Author

Ardakan University

Abstract

The Tower of Hanoi problem is a historically rooted problem, and it was formulated by the French mathematician Lucas. In this article, we present the famous Tower of Hanoi problem and its generalization. We explore the optimal solutions to these problems using recursive methods and based on graph theory. It is demonstrated that the graph resulting from solving the Tower of Hanoi problem, along with its corresponding graph, is the Sierpinski fractal.

Keywords


[1] A. Babolian, Topics in Discrete Mathematics, Mobtakeran, 1996.
[2] S. Kordrostami, R. Ahmadzadeh Gerami , A, ghane and S. Poorjafar, A review on Hanoi tower and a new formola,Journal of Operational Research in Its Applications, 4 (2007) 41-47‎.
 
[3] A. Mashhadi, K. Rasoolzadeh Tabatabaei, P. Azadfallah and A. soltanifar,Planning and organization ability in children with attention deficit hyperactivity disorder, Journal of Educational Psychology Studies, 11 (2010) 151-170.
[4] S. Epp, Discrete Mathematics: Introduction to Mathematical Reasoning, Nelson Education, 2011.
[5] A. M. Hinz and et. al., The Tower of Hanoi–Myths and Maths, Springer Science Business Media, 2013.
[6] E. Rufati, B. Rahmani and B. Percinkova, Analysis of Recursive Algorithms for Solving the Problemof the Tower of Hanoi, Anglisticum Journal, 2 (2016) 12–18.
[7] M. Shinoda, E. Teufl and S. Wagner, Uniform spanning trees on Sierpinski graphs, Lat. Am. J. Probab. Math. Stat., 11 (2014) 737-780.
[8] E. Lucas, Recrations Mathematiques, 3, Gauthier-Villars, Paris, 1893.
[9] J. P. Allouche, D. Astoorian, J. Randall and J. Shallit, Morphisms, squarefree strings, and the tower of Hanoi puzzle, Amer. Math. Monthly, 101 (1994) 651–658.
[10] E. L. Spitznagel, Selected topics in mathematics, Holt, Rinehart and Winston, 1971.
[11] E. Vakil, M. Lowe and C. Goldfus, Performance of Children With Developmental Dyslexia on Two Skill Learning Tasks—Serial Reaction Time and Tower of Hanoi Puzzle A Test of the Specific Procedural Learning Difficulties Theory, J. Learn. Disabil., 48 (2015) 471–481.
[12] R. Bull, K. A. Espy and T. E. Senn, A comparison of performance on the Towers of London and Hanoi in young children, J. Child. Psychol. Psychiatry, 45 (2004) 743–754.
[13] R. Snapp, Tower of Hanoi, Lecture Notes for CS 5, 2005.
[14] B. A. Brousseau, Tower of Hanoi with more pegs, J. Recr. Math., 8 (1975-76) 169–176.
[15] M. K. Lee, The graph for the Tower of Hanoi with four pegs, Pythagoras, 57 (2003) 27–31.
[16] A. M. Hinz and P. Daniele, On the planarity of Hanoi graphs, Expo. Math., 20 (2002) 263–268.
[17] C. A. Knoblock, Abstracting the tower of Hanoi, Working Notes of AAAI-90 Workshop on Automatic Generation of Approximations and Abstractions, 1990.
[18] H. Masum, S. Christensen and F. Oppacher, The Turing Ratio: Metrics For Open-ended Tasks, Proceedings of the Genetic and Evolutionary Computation Conference, New York, USA, 2002.
Volume 2, Issue 3 - Serial Number 3
September 2017
Pages 23-36
  • Receive Date: 22 February 2016
  • Revise Date: 01 October 2016
  • Accept Date: 18 January 2017
  • Publish Date: 22 November 2017