Generalizations of the Hanoi Towers Problem

TL;DR

This paper explores generalizations of the classical Hanoi Towers problem, including new legal positions and constrained move versions, aiming to find optimal move sequences and analyze various problem variants.

Contribution

It introduces new problem variants allowing previously illegal positions and studies constrained move versions, providing insights into optimal solutions and problem complexity.

Findings

Identified optimal move sequences for new problem variants

Analyzed constraints and their impact on solution length

Compared classical and generalized problem complexities

Abstract

Our theme bases on the classical Hanoi Towers Problem. In this paper we will define a new problem, permitting some positions, that were not legal in the classical problem. Our goal is to find an optimal (shortest possible) sequence of discs' moves. Besides that, we will research all versions of 3-pegs classical problem with some special constraints, when some types of moves are disallowed.