In How Many Steps the k Peg Version of the Towers of Hanoi Game Can Be Solved?
نویسنده
چکیده
In this we paper we consider the version of the classical Towers of Hanoi games where the game-board contains more than three pegs. For k pegs we give a 2k 1/(k−2) lower bound on the number of steps necessary for transferring n disks from one peg to another. Apart from the value of the constants Ck this bound is tight.
منابع مشابه
What is the least number of moves needed to solve the 4-peg Towers of Hanoi problem?
We prove that the solutions to the k-peg Tower of Hanoi problem given by Frame and Stewart are minimal. This paper solves the problem of finding the least number of moves needed to transfer a Tower of Hanoi of n disks, from an initial peg to another one of the k− 1 other pegs. This problem generalizes a well known puzzle proposed and solved in [5] for the case of three pegs. The generalization ...
متن کاملModified Hanoi Towers Groups and Limit Spaces
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 groups, H (k) c , and show that these are the unique maximal contracting Hanoi groups under a suitable symmetry condition. Finally, we provide partial results...
متن کاملTwin Towers of Hanoi
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 chosen pegs (the smallest disk from one of the pegs is moved to the other peg), but also, simultaneously, between the corresponding pair of pegs in the cou...
متن کاملHamiltonianicity of the Towers of Hanoi Problem
In this paper we analyze a variant of the n-disk Towers of Hanoi problem with an arbitrary starting and ending configuration using transition graphs representing valid configurations. In particular, we show that starting with any configuration, there is a sequence of moves that goes through each valid configuration exactly once and back to the starting configuration. Also, we show how the origi...
متن کاملOn the Frame--Stewart Conjecture about the Towers of Hanoi
The multipeg Towers of Hanoi problem consists of k pegs mounted on a board together with n disks of different sizes. Initially these disks are placed on one peg in the order of their size, with the largest at the bottom. The rules of the problem allow disks to be moved one at a time from one peg to another as long as a disk is never placed on top of a smaller disk. The goal of the problem is to...
متن کامل