A Note on the Tower of Hanoi Problem with Evildoers

Authors

  • S. M. Shahidul Islam HSTU
  • A. A. K. Majumdar Ritsumeikan Asia-Pacific University

DOI:

https://doi.org/10.18034/ei.v9i1.515

Keywords:

Divine rule, evildoer, Hanoi tower problem

Abstract

Recent literature considers the variant of the classical Tower of Hanoi problem with n (³ 1) discs, where r (1 £ r < n) discs are evildoers, each of which can be placed directly on top of a smaller disc any number of times. Letting E(n, r) be the minimum number of moves required to solve the new variant, an explicit form of E(n, r) is available which depends on a positive integer constant N. This study investigates the properties of N.

 

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Author Biographies

  • S. M. Shahidul Islam, HSTU

    Professor & Chair, Department of Mathematics, Hajee Mohammad Danesh Science and Technology University, Dinajpur-5200, Bangladesh

  • A. A. K. Majumdar, Ritsumeikan Asia-Pacific University

    Ritsumeikan Asia-Pacific University, Renace Beppu 205, Beppu-shi 874-0842, JAPAN

References

Chen, X., Tian, B. and Wang, L. (2007). Santa Claus’ Towers of Hanoi, Graphs and Combinatorics, 23 (Supplement), 153-167. DOI: https://doi.org/10.1007/s00373-007-0705-4

Hinz, A.M., Klavzar, S. and Petr, C. (2018). The Tower of Hanoi – Myths and Maths, Springer, Basel. DOI: https://doi.org/10.1007/978-3-319-73779-9

Majumdar, A.A.K. (2012). The Classical Tower of Hanoi Problem and Its Generalizations, Vol. 1: Multi-Peg Generalizations. Lambert Academic Publishing, U.S.A.

Majumdar, A.A.K. (2013). The Classical Tower of Hanoi Problem and Its Generalizations, Vol. 2: Other Generalizations, Lambert Academic Publishing, U.S.A.

Majumdar, A.A.K. (2018). The Classical Tower of Hanoi Problem and Its Generalizations, Vol. 3: Miscellaneous Topics, Lambert Academic Publishing, U.S.A.

Majumdar, A.A.K. (2019). The Tower of Hanoi Problem with Evildoer Discs. Journal of Bangladesh Academy of Sciences 43(2), 205-209. DOI: https://doi.org/10.3329/jbas.v43i2.45742

Majumdar, A.A.K. and Islam, S.M.S. (2019). The tower of Brahma with one evildoer: the life-time of the world, HSTU Journal of Science and Technology 17, 111-118.

Majumdar, A.A.K. and Islam, S.M.S. (2020). On the sinner's tower of Hanoi, HSTU Journal of Science and Technology 18, 85-92.

Wu, J.S. and Chen, R.J. (1993). The Towers of Problem with Cyclic Parallel Moves, Information Processing Letters 46(1), 1-6. DOI: https://doi.org/10.1016/0020-0190(93)90187-E

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Published

2021-04-01

Issue

Vol. 9 No. 1 (2021): January - June Issue

Section

Peer Reviewed Articles

License

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How to Cite

Islam, S. M. S. ., & Majumdar, A. A. K. . (2021). A Note on the Tower of Hanoi Problem with Evildoers. Engineering International, 9(1), 21-28. https://doi.org/10.18034/ei.v9i1.515