The Towers of Fibonacci, Lucas, Jacobsthal, and Pell, and Their Associated Graphs
Abstract
This paper introduces four novel variants of the classical Tower of Hanoi problem, each inspired by a well-known integer sequence: Fibonacci, Lucas, Jacobsthal, and Pell. These variants incorporate a new type of move, termed the magic move, which extends the classical rules of the Tower of Hanoi, and establishes a direct correspondence with the recursive structure of each sequence. The paper provides a combinatorial analysis of these variants, including the derivation of recurrence relations for the length of optimal solutions, characterizations of solution structures, and enumeration of optimal and feasible solutions. Furthermore, for each variant, a family of associated graphs is defined and analyzed, highlighting their recursive structures and some of their properties such as connectivity and planarity.
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Publication details
- Journal / source
- The Fibonacci Quarterly
- Publisher
- Informa UK Limited
- Volume
- 64
- Issue
- 2
- Pages
- 319–349
- Publication date
- 8 January 2026
- Language
- EN