A new lower bound for the Towers of Hanoi problem

TL;DR

This paper improves the asymptotic lower bound on the minimum number of moves required for the Towers of Hanoi problem with p pegs, extending recent breakthroughs and applying new ideas to all p >= 5.

Contribution

It introduces an asymptotic improvement on the lower bound for the multi-peg Towers of Hanoi problem using ideas inspired by Bousch's 2014 solution.

Findings

Improved asymptotic lower bound for p >= 5

Extension of Bousch's ideas to general p

Enhanced understanding of the problem's complexity

Abstract

More than a century after its proposal, the Towers of Hanoi puzzle with 4 pegs was solved by Thierry Bousch in a breakthrough paper in 2014. The general problem with p pegs is still open, with the best lower bound on the minimum number of moves due to Chen and Shen. We use some of Bousch's new ideas to obtain an asymptotic improvement on this bound for all p >= 5.