【摘要】 194 1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。更多还原

【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.更多还原