How to Move the Discs on the Tower of Hanoi
- 数学科学－已发表论文 
Hanoi塔问题自提出以来已有一百多年的历史．其间，这一问题吸引了许多的研究者．正如H.A.Simon所指出的，Hanoi塔问题对于认知科学就象大肠杆菌对现代基因学那样，是一个无价的研究标本．事实上，它已成为组合数学，人工智能，计算机科学以及规划等中的递归问题的典型例子，并由此产生了各种各样成熟的算法．回顾这些结果，我们提出一个基本问题：能否对Hanoi塔问题给出一个公式解？本文就此给出了一个肯定的回答．在我们的研究中，图论将是一个有力的工具The primary version of the Tower of Hanoi problem (puzzle) was firstly invented by E.Lucas in 1883,and later was numbered by"problem 3918"(with 3 pegs).The general version was introduced by Wood,Gerety and Cull.As pointed out by H.A. Simon,the tower (of Hanoi) was to cognitive science what the bacteria,E.coli,were to modern genetics-an invaluable standard research setting.During the past 100 years or more,this puzzle has attracted more attentions of,not only the mathematicians', but also the computer scientists'. A large number of various (recursive, iterative, cyclic and loopless etc.) algorithms for solving this puzzle were established. Reviewing the previous literatures, it leads naturally to an elementary question: is it possible to find an algebraic formula (non-algorithm) for this problem? Here we show that the answer is "Yes".