A Recurrence Relation Related to the Reve’s Puzzle

Reve’s Puzzle Related Recurrence

Authors

  • Abdullah-Al-Kafi Majumdar Department of Mathematics, Jahangirnagar University, Savar, Dhaka 1342, Bangladesh

Keywords:

Reve’s puzzle, Recurrence relation, Local-value relationships

Abstract

In a recent paper, Majumdar [1] studied, to some extent, the generalized recurrence relation, introduced by Matsuura
[2] :
( )  ( ) 2 1
1
s MT n, min MT n s, ,
s n
      
 
where n ≥ 1 and  ≥ 2 are integers. It may be mentioned here that,  = 2 corresponds to the Reve’s puzzle, introduced by Dudeney
[3]. In this paper, we study more closely the properties of the function MT(n,  ), and give a closed-form expression of it when
 = 2i (for any integer i ≥ 2).

References

A.A.K. Majumdar. Some Local-Value Relationships for the Recurrence Relation Related to the Tower of Hanoi Problem, Proceedings of the Pakistan Academy of Sciences, A: Physical and Computational Sciences, 53(2): 187 – 201 (2016).

A. Matsuura. Exact Analysis of the Recurrence Relations Generalized from the Tower of Hanoi. SIAM Proceedings in Applied Mathematics, 129: 228 – 233 (2008).

H.E. Dudeney. The Canterbury Puzzles. Thomas Nelson and Son London (4th Ed. by Dover, 1958).

T.R. Roth. The Tower of Brahma Revisited. J. Recreational Mathematics, 7(2): 116  119 (1974).

A.M. Hinz. An Iterative Algorithm for the Tower of Hanoi with Four Pegs. Computing, 42:133  140 (1989).

A.A.K. Majumdar. The Generalized Four-Peg Tower of Hanoi Problem. Optimization, 29: 349  360 (1994).

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

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Published

2021-03-15

How to Cite

Majumdar, A.-A.-K. . (2021). A Recurrence Relation Related to the Reve’s Puzzle: Reve’s Puzzle Related Recurrence. Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, 56(4), 63–74. Retrieved from http://ppaspk.org/index.php/PPAS-A/article/view/54

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