The Preliminary Probe of 4-Peg Hanoi Tower

Abstract

Abstract: In 1941,J.S.Frame gave out an algorithm in American Mathematical Monthly to solve the problem of 4-peg Hanoi Tower, but he did not provide the proof for the final formulae. According to that algorithm, this article puts forward a formula to calculate the number of movements necessary for the 4-peg Hanoi Tower problem, and proves it using mathematical induction.

Key words: 4-peg Hanoi Tower, zone, the number of remaining disks R(n)

摘要： 1941年，J.S.Frame在《美国数学月刊》上提出了一种解决四柱汉诺塔问题的算法，但未给出最终公式的证明。本文按照这种算法总结出完成四柱汉诺塔游戏之最少步数的公式，并用数学归纳法证明了它。

关键词: 四柱汉诺塔, 区, 剩余盘数R(n)

CLC Number:

O224

YANG Kai,XU Chuan. The Preliminary Probe of 4-Peg Hanoi Tower[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

杨楷, 徐川. 四柱汉诺塔之初步探究[J]. 北京大学学报（自然科学版）.

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URL: https://xbna.pku.edu.cn/EN/

https://xbna.pku.edu.cn/EN/Y2004/V40/I1/99

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The Preliminary Probe of 4-Peg Hanoi Tower

四柱汉诺塔之初步探究

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