**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31533

##### On the Solution of the Towers of Hanoi Problem

**Authors:**
Hayedeh Ahrabian,
Comfar Badamchi,
Abbass Nowzari-Dalini

**Abstract:**

**Keywords:**
Loopless algorithm,
Binary tree,
Towers of Hanoi.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1076656

**References:**

[1] M. D. Atkinson, The cyclic towers of Hanoi, Inform. Process. Lett. 13 (1981), 118-119.

[2] P. Buneman and L. Levy, The towers of Hanoi problem, Inform. Process. Lett. 10 (1980), 243-244.

[3] X. Chen and J. Shen, On the Frame-Stewart conjecture about the towers of Hanoi, SIAM J. Comput. 33 (2004), 584-589.

[4] H. Dudeney, The Canterbury Puzzles, Thomas Nelson & Sons, London, 1907.

[5] E. W. Dijkstra, A Short Introduction to the Art of Programming, Technisch Hogeschool Eindhoven, EWD 316, 1971.

[6] M. C. Er, A linear space algorithm for the towers of Hanoi problem by using a virtual disc, Inform. Sci. 47 (1989), 47-52.

[7] M. C. Er, A loopless and optimal algorithm for the cycle for Hanoi problem, Inform. Sci. 42 (1987), 283-287.

[8] M. C. Er, A loopless approach for constructing a fastest algorithm for the towers of Hanoi problem, Intern. J. Comput. Math. 20 (1986), 49-54.

[9] M. C. Er, The towers of Hanoi and binary numerals, J. Inform. Optim. Sci. 6 (1985), 147-152.

[10] J. S. Frame, Solution to advanced problem 3918, Amer. Math. Monthly 48 (1941), 216-217.

[11] T. D. Gedeon, The cyclic towers of Hanoi: An iterative solution produced by transformation, Copmut. J. 39 (1996), 353-356.

[12] P. Gupta, P. P. chakrabarti, and S. Ghose, The towers of Hanoi: Generalizations, specializations and algorithms, Intern. J. Comput. Math. 46 (1992), 149-161.

[13] P. J. Hayes, A note on the towers of Hanoi problem, Copmut. J. 20 (1977), 282-285.

[14] S. Klav╦åzar, U. Milutinovi'c, and C. Petr, On the Frame-Stewart algorithm for the multi-peg towers of Hanoi problem, Discrete Appl. Math. 120 (2002), 141-157.

[15] S. Klav╦åzar and U. Milutinovi'c, Simple Explicit Formulas for the Frame- Stewart Numbers, Ann. Comb. 6 (2002), 157-167

[16] H. Mayer and D. Perkins, Towers of Hanoi revisited, SIGPLAN Notices 19 (1984), 80-84.

[17] S. Maziar, Solution of the tower of Hanoi problem using a binary tree, SIGPLAN Notice 20 (1985), 16-20.

[18] B. Meyer, A note on iterative Hanoi, SIGPLAN Notices 19 (1984), 123- 126.

[19] P. H. Schoute, De ringen van brahma, Eigen Harrd 22 (1884), 274-276.

[20] M. Sniedovich, OR/MS games: 2. Towers of Hanoi, INFORMS Transcations on Education 3 (2002), 34.

[21] B. M. Stewart, Advanced problem 3918, Amer. Math. Monthly 46 (1939), 363-363.

[22] B. M. Stewart, Solution to advanced problem 3918, Amer. Math. Monthly 48 (1941), 217-219.

[23] P. K. Stockmeyer, C. D. Bateman, J. W. Clark, C. R. Eyster, M. T. Harrison, N. A. Loehr, P. J. Rodriguez, and J. R. Simmons, Exchanging disks in the tower of Hanoi, Intern. J. Comput. Math. 59 (1995), 37-47.

[24] M. Saegedy, In how many steps the k peg version of the towers of Hanoi game can be solved, Lec. Note. Comput. Sci. 1563 (1999) 356-361.

[25] T. R. Walsh, The towers of Hanoi revisited: Moving the rings by counting the moves, Inform. Process. Lett. 15 (1982), 64-67.

[26] L. Xue-miao, A loopless approach to the multipeg towers of Hanoi, Intern. J. Comput. Math. 33 (1990) 13-29.