4杆汉诺塔问题

The Hanoi-tower Problem with More Poles

通常汉诺塔问题只考虑带3根杆,当圆盘数为n时,最佳方案的移动次数为H(n)=2 n?1。本文考虑带4杆的汉诺塔问题及其移动方案[(1?α),α,0,0]。一个有趣的问题是:对于0<α<1,当α取什么值时,n≥240时,最优方案的α值稳定在0.9。

The usual Hanoi-tower game is played with three poles. The optimal moving number is H （ n ） = 2＂ - 1 in the game with n discs. In this paper, the Hanoi-tower problem with four poles is considered, and the corresponding solution [（1 - a）, a, 0, 0] is given. An interesting problem is how to take a-value （0 〈 a 〈 1 ） would make the solution [（1-a）,a,0,0] to be an optimal. The experiments show that a is greater as the number of disc n increased in the optimal solution [（1- a）, a, 0, 0]. And a- value in the optimal solution will stables at 0.9 for n 〉 240