Statements: This blog was written by me, but most of content  is quoted from book【Data Structure with Java Hubbard】 

【Description】

 we have seen important examples of functions that are more naturally defined and more easily understood by using recursion. Foe some problem, recursion is the only reasonable method of solution.The towers of hanoi puzzle is a classical example of a problem whose solution demands recursion. The game consists of a board with three vertical pegs labeled A, B, and C, and a sequence of n disks with holes in their centers. The radii of the disks are in an arithmetic progression(eg,6cm, 7cm, 8cm); and are mounted on peg A. The rule is that no disk may be above a smaller disk on the same peg. The objective of the game is to move all the disks from peg A to peg C, one disk at a time, without violating the rule. 

【Implement】

package com.albertshao.ds.recursion;

//  Data Structures with Java, Second Edition
//  by John R. Hubbard
//  Copyright 2007 by McGraw-Hill


public class TestHanoiTowers {
  public static void main(String[] args) {
    HanoiTowers(3, 'A', 'B', 'C');
  }
  
  public static void HanoiTowers(int n, char x, char y, char z) {
    if (n==1) {                // basis
      System.out.printf("Move top disk from peg %c to peg %c.%n", x, z);
    } else {              
      HanoiTowers(n-1, x, z, y);  // recursion
      HanoiTowers(1, x, y, z);    // recursion  
      HanoiTowers(n-1, y, x, z);  // recursion
    }
  }
}

Move top disk from peg A to peg C.
Move top disk from peg A to peg B.
Move top disk from peg C to peg B.
Move top disk from peg A to peg C.
Move top disk from peg B to peg A.
Move top disk from peg B to peg C.
Move top disk from peg A to peg C.