Related papers: On the restricted Hanoi Graphs
The famous Tower of Hanoi puzzle involves moving $n$ discs of distinct sizes from one of $p\geq 3$ pegs (traditionally $p=3$) to another of the pegs, subject to the constraints that only one disc may be moved at a time, and no disc can ever…
We introduce and study a new four-peg variant of the Tower of Hanoi problem under parity constraints. Two pegs are neutral and allow arbitrary disc placements, while the remaining two pegs are restricted to discs of a prescribed parity: one…
The generalized Tower of Hanoi problem with h \ge 4 pegs is known to require a sub-exponentially fast growing number of moves in order to transfer a pile of n disks from one peg to another. In this paper we study the Path_h variant, where…
The objective of the well-known Towers of Hanoi puzzle is to move a set of disks one at a time from one of a set of pegs to another, while keeping the disks sorted on each peg. We propose an adversarial variation in which the first player…
In the Twin Towers of Hanoi version of the well known Towers of Hanoi Problem there are two coupled sets of pegs. In each move, one chooses a pair of pegs in one of the sets and performs the only possible legal transfer of a disk between…
The weighted Tower of Hanoi is a new generalization of the classical Tower of Hanoi problem, where a move of a disc between two pegs $i$ and $j$ is weighted by a positive real $w_{ij}\geq 0$. This new problem generalizes the concept of…
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…
We prove the exact formulae for the expected number of moves to solve several variants of the Tower of Hanoi puzzle with 3 pegs and n disks, when each move is chosen uniformly randomly from the set of all valid moves. We further present an…
Considering the symmetries and self similarity properties of the corresponding labeled graphs, it is shown that the minimal number of moves in the Tower of Hanoi game with $p =4$ pegs and $n \geq p$ disks satisfies the recursive formula $…
We introduce the $k$-peg Hanoi automorphisms and Hanoi self-similar groups, a generalization of the Hanoi Towers groups, and give conditions for them to be contractive. We analyze the limit spaces of a particular family of contracting Hanoi…
Finite dimensional representations of the Hanoi Towers group are used to calculate the spectra of the finite graphs associated to the Hanoi Towers Game on three pegs (the group serves as a renorm group for the game). These graphs are…
The Frame-Stewart conjecture states the least number of moves to solve a generalized Tower of Hanoi problem, of n disks and p pegs. In this paper, we prove a weaker version of the Frame-Stewart conjecture.
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…
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…
The Tower of Hanoi continues to provide a surprisingly rich meeting point for recursive reasoning, combinatorial geometry, and computational verification. Motivated by the editorial standards of the Bulletin of the Australian Mathematical…
The Tower of Hanoi game is a classical puzzle in recreational mathematics (Lucas 1883) which also has a strong record in pure mathematics. In a borderland between these two areas we find the characterization of the minimal number of moves,…
In this paper, our aim is to prove that our recursive algorithm to solve the "Reve's puzzle" (four- peg Tower of Hanoi) is the optimal solution according to minimum number of moves. Here we used Frame's five step algorithm to solve the…
We present in this paper four new variants of the Tower of Hanoi problem, the optimal solution of each of these variants is related to one of the four known numbers Fibonacci, Lucas, Pell, and Jacobsthal. We give an optimal solution to each…
In the Tower of Hanoi problem, there is six types of moves between the three pegs. The main purpose of the present paper is to find out the number of each of these six elementary moves in the optimal sequence of moves. We present a…
The number of spanning trees of a graph is an important invariant related to topological and dynamic properties of the graph, such as its reliability, communication aspects, synchronization, and so on. However, the practical enumeration of…