益智游戏“汉诺塔”中的矩阵运算

汉诺塔(Tower of Hanoi)问题源于印度一个古老传说,据此做成了益智游戏,蕴含大量的数学思想与方法.本文采用矩阵描述汉诺塔状态和圆盘移动过程,将圆盘从一个位置移动到另一个位置转化为矩阵的加法,进而构造由若干可能状态矩阵组成的图的邻接矩阵,计算其幂矩阵,由此很方便地求得完成汉诺塔游戏的所有可能的圆盘移动方案,求解过程简单,含义清晰,易于理解和实现.

Matrix Operations in the Puzzle of Hanoi Tower

Tower of Hanoi is an puzzle originated from an ancient Indian legend,and that creates a puzzle,it bears rich mathematical theories behind it.In this paper,we focus on the matrix operation for solving the puzzle.We use matrix to describe the states of the tower and the transportation of the discs,use matrix addition to describe the transportation process of a disc from one position to another position.Moreover,we define the adjacent matrix of the set of possible state matrices,calculate its power matrices,and identify all the possible transportation strategies for accomplishing the transportation task.The proposed method is simple and easy for understanding as well as in implementation.