Solutions to the generalized Towers of Hanoi problem
Mikael Erik J\"orgensen
TL;DR
This paper proves the Frame-Stewart algorithm for the generalized Towers of Hanoi, determines the minimal move count, and explores the characteristics of optimal solutions, advancing understanding of this classic puzzle.
Contribution
It provides a formal proof of the Frame-Stewart algorithm and analyzes the optimal move strategies for the generalized Towers of Hanoi problem.
Findings
Proof of the Frame-Stewart algorithm
Exact number of moves for optimal solutions
Analysis of multiple optimal solutions
Abstract
The purpose of this paper is to prove the Frame-Stewart algorithm for the generalized Towers of Hanoi problem as well as finding the number of moves required to solve the problem and studying the multitude of optimal solutions. The main idea is to study how to most effectively move away all but the last disc and use the fact that the total number of moves required to solve the problem is twice this number plus one.
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Taxonomy
TopicsStructural Analysis and Optimization