What is the least number of moves needed to solve the k-peg Towers of Hanoi problem?

TL;DR

This paper proves that the solutions proposed by Frame and Stewart for the k-peg Towers of Hanoi problem are indeed minimal, confirming their optimality for solving the puzzle.

Contribution

It establishes the minimality of the Frame-Stewart solutions for the k-peg Towers of Hanoi problem, resolving a longstanding question.

Findings

Frame-Stewart solutions are minimal for the k-peg problem

Proof confirms optimality of existing solutions

Advances understanding of combinatorial puzzle complexity

Abstract

We prove that the solutions to the k-peg Tower of Hanoi Problem given by Frame and Stewart are minimal.