这个游戏的目标是,借助Y塔,将X塔上的所有盘子移到Z塔上。但一次只准移动一个盘子,而且只准把小盘子压在大盘子上,而不允许将大盘子压在小盘子上。
这看起来似乎很麻烦,难道不是吗?但实际上3个盘子还是很好办的,7步。(2个盘子最好办),但是汉诺塔有他的难度等级,有些疯子甚至喜欢玩11阶、甚至是16阶汉诺塔。
这听起来好像很简单,真的吗?以下是8阶汉诺塔的解法:(255步) 8阶汉诺塔解法0.
1.X ==> Y
2.X ==> Z
3.Y ==> Z
4.X ==> Y
5.Z ==> X
6.Z ==> Y
7.X ==> Y
8.X ==> Z
9.Y ==> Z
10.Y ==> X
11.Z ==> X
12.Y ==> Z
13.X ==> Y
14.X ==> Z
15.Y ==> Z
16.X ==> Y
17.Z ==> X
18.Z ==> Y
19.X ==> Y
20.Z ==> X
21.Y ==> Z
22.Y ==> X
23.Z ==> X
24.Z ==> Y
25.X ==> Y
26.X ==> Z
27.Y ==> Z
28.X ==> Y
29.Z ==> X
30.Z ==> Y
31.X ==> Y
32.X ==> Z
33.Y ==> Z
34.Y ==> X
35.Z ==> X
36.Y ==> Z
37.X ==> Y
38.X ==> Z
39.Y ==> Z
40.Y ==> X
41.Z ==> X
42.Z ==> Y
43.X ==> Y
44.Z ==> X
45.Y ==> Z
46.Y ==> X
47.Z ==> X
48.Y ==> Z
49.X ==> Y
50.X ==> Z
51.Y ==> Z
52.X ==> Y
53.Z ==> X
54.Z ==> Y
55.X ==> Y
56.X ==> Z
57.Y ==> Z
58.Y ==> X
59.Z ==> X
60.Y ==> Z
61.X ==> Y
62.X ==> Z
63.Y ==> Z
64.X ==> Y
65.Z ==> X
66.Z ==> Y
67.X ==> Y
68.Z ==> X
69.Y ==> Z
70.Y ==> X
71.Z ==> X
72.Z ==> Y
73.X ==> Y
74.X ==> Z
75.Y ==> Z
76.X ==> Y
77.Z ==> X
78.Z ==> Y
79.X ==> Y
80.Z ==> X
81.Y ==> Z
82.Y ==> X
83.Z ==> X
84.Y ==> Z
85.X ==> Y
86.X ==> Z
87.Y ==> Z
88.Y ==> X
89.Z ==> X
90.Z ==> Y
91.X ==> Y
92.Z ==> X
93.Y ==> Z
94.Y ==> X
95.Z ==> X
96.Z ==> Y
97.X ==> Y
98.X ==> Z
99.Y ==> Z
100.X ==> Y
101.Z ==> X
102.Z ==> Y
103.X ==> Y
104.X ==> Z
105.Y ==> Z
106.Y ==> X
107.Z ==> X
108.Y ==> Z
109.X ==> Y
110.X ==> Z
111.Y ==> Z
112.X ==> Y
113.Z ==> X
114.Z ==> Y
115.X ==> Y
116.Z ==> X
117.Y ==> Z
118.Y ==> X
119.Z ==> X
120.Z ==> Y
121.X ==> Y
122.X ==> Z
123.Y ==> Z
124.X ==> Y
125.Z ==> X
126.Z ==> Y
127.X ==> Y
128.X ==> Z
129.Y ==> Z
130.Y ==> X
131.Z ==> X
132.Y ==> Z
133.X ==> Y
134.X ==> Z
135.Y ==> Z
136.Y ==> X
137.Z ==> X
138.Z ==> Y
139.X ==> Y
140.Z ==> X
141.Y ==> Z
142.Y ==> X
143.Z ==> X
144.Y ==> Z
145.X ==> Y
146.X ==> Z
147.Y ==> Z
148.X ==> Y
149.Z ==> X
150.Z ==> Y
151.X ==> Y
152.X ==> Z
153.Y ==> Z
154.Y ==> X
155.Z ==> X
156.Y ==> Z
157.X ==> Y
158.X ==> Z
159.Y ==> Z
160.Y ==> X
161.Z ==> X
162.Z ==> Y
163.X ==> Y
164.Z ==> X
165.Y ==> Z
166.Y ==> X
167.Z ==> X
168.Z ==> Y
169.X ==> Y
170.X ==> Z
171.Y ==> Z
172.X ==> Y
173.Z ==> X
174.Z ==> Y
175.X ==> Y
176.Z ==> X
177.Y ==> Z
178.Y ==> X
179.Z ==> X
180.Y ==> Z
181.X ==> Y
182.X ==> Z
183.Y ==> Z
184.Y ==> X
185.Z ==> X
186.Z ==> Y
187.X ==> Y
188.Z ==> X
189.Y ==> Z
190.Y ==> X
191.Z ==> X
192.Y ==> Z
193.X ==> Y
194.X ==> Z
195.Y ==> Z
196.X ==> Y
197.Z ==> X
198.Z ==> Y
199.X ==> Y
200.X ==> Z
201.Y ==> Z
202.Y ==> X
203.Z ==> X
204.Y ==> Z
205.X ==> Y
206.X ==> Z
207.Y ==> Z
208.X ==> Y
209.Z ==> X
210.Z ==> Y
211.X ==> Y
212.Z ==> X
213.Y ==> Z
214.Y ==> X
215.Z ==> X
216.Z ==> Y
217.X ==> Y
218.X ==> Z
219.Y ==> Z
220.X ==> Y
221.Z ==> X
222.Z ==> Y
223.X ==> Y
224.X ==> Z
225.Y ==> Z
226.Y ==> X
227.Z ==> X
228.Y ==> Z
229.X ==> Y
230.X ==> Z
231.Y ==> Z
232.Y ==> X
233.Z ==> X
234.Z ==> Y
235.X ==> Y
236.Z ==> X
237.Y ==> Z
238.Y ==> X
239.Z ==> X
240.Y ==> Z
241.X ==> Y
242.X ==> Z
243.Y ==> Z
244.X ==> Y
245.Z ==> X
246.Z ==> Y
247.X ==> Y
248.X ==> Z
249.Y ==> Z
250.Y ==> X
251.Z ==> X
252.Y ==> Z
253.X ==> Y
254.X ==> Z
255.Y ==> Z
从前,有一个人叫A,他看到3阶汉诺塔毫无头绪。他有一堆帮手。
有一天这个A先生突发奇想,他想:我现在不知道3阶汉诺塔怎么移动到Z,但是要是有一个人帮我把X塔上的上面2个盘子移动到Y塔,我岂不是只需要移动最后一个盘子,然后再让他用同样的方法把Y塔上的2个盘子移动到Z上,问题不就解决了???
于是他命令B把2个盘子移动到Y上去……结果哪知道这B居然不知道怎么移。但他想:我现在不知道2阶汉诺塔怎么移动到Y,但是要是有一个人帮我把X塔上的上面1个盘子移动到Z塔,我岂不是只需要移动最后一个盘子,然后再让他用同样的方法把Z塔上的1个盘子移动到Y上?
……………………
……………………
于是问题就解决了!就像这样↓ 3阶汉诺塔解法0.
1.X ==> Z
2.X ==> Y
3.Z ==> Y
4.X ==> Z
5.Y ==> X
6.Y ==> Z
7.X ==> Z