【Java/算法/组合】将20把相同的椅子分别放入编号为1，2，3，4的四个会议室内，要求每个会议室中放入的椅子数不小于它的编号数，问有多少种不同的放法？

【数学解法】

先将0张椅子放入1号房间，1张椅子放入2号房间，2张椅子放入3号房间，3张椅子放入4号房间,这以后再放椅子就不存在违背题设的情况了。

剩下十四张椅子分四份，相当于3个隔板去插十四张椅子中的13个空，那么方案是C13_3=13*12*11/321=13*11*2=286

【代码解法】

这个程序实际只需要找到和为14的四个自然数，完成此任务只需四重循环即可，不需要Combination组合器的参与。

得到这四个数后，加上0，1，2，3输出即可。

代码：

public class RoomChair {
    public static void main(String[] args){
        int idx=0;
        for(int i=1;i<=13;i++){
            for(int j=1;j<=13;j++){
                for(int k=1;k<=13;k++){
                    for(int m=1;m<=13;m++) {
                        if (i + j + k+m == 14) {
                            System.out.println(String.format("%03d", ++idx) + ".Room1:" + (i+0) + " Room2:" + (j+1) + " Room3:"+ (k+2)+" Room4:" + (m+3));
                        }
                    }
                }
            }
        }
    }
}

【输出】

001.Room1:1 Room2:2 Room3:3 Room4:14
002.Room1:1 Room2:2 Room3:4 Room4:13
003.Room1:1 Room2:2 Room3:5 Room4:12
004.Room1:1 Room2:2 Room3:6 Room4:11
005.Room1:1 Room2:2 Room3:7 Room4:10
006.Room1:1 Room2:2 Room3:8 Room4:9
007.Room1:1 Room2:2 Room3:9 Room4:8
008.Room1:1 Room2:2 Room3:10 Room4:7
009.Room1:1 Room2:2 Room3:11 Room4:6
010.Room1:1 Room2:2 Room3:12 Room4:5
011.Room1:1 Room2:2 Room3:13 Room4:4
012.Room1:1 Room2:3 Room3:3 Room4:13
013.Room1:1 Room2:3 Room3:4 Room4:12
014.Room1:1 Room2:3 Room3:5 Room4:11
015.Room1:1 Room2:3 Room3:6 Room4:10
016.Room1:1 Room2:3 Room3:7 Room4:9
017.Room1:1 Room2:3 Room3:8 Room4:8
018.Room1:1 Room2:3 Room3:9 Room4:7
019.Room1:1 Room2:3 Room3:10 Room4:6
020.Room1:1 Room2:3 Room3:11 Room4:5
021.Room1:1 Room2:3 Room3:12 Room4:4
022.Room1:1 Room2:4 Room3:3 Room4:12
023.Room1:1 Room2:4 Room3:4 Room4:11
024.Room1:1 Room2:4 Room3:5 Room4:10
025.Room1:1 Room2:4 Room3:6 Room4:9
026.Room1:1 Room2:4 Room3:7 Room4:8
027.Room1:1 Room2:4 Room3:8 Room4:7
028.Room1:1 Room2:4 Room3:9 Room4:6
029.Room1:1 Room2:4 Room3:10 Room4:5
030.Room1:1 Room2:4 Room3:11 Room4:4
031.Room1:1 Room2:5 Room3:3 Room4:11
032.Room1:1 Room2:5 Room3:4 Room4:10
033.Room1:1 Room2:5 Room3:5 Room4:9
034.Room1:1 Room2:5 Room3:6 Room4:8
035.Room1:1 Room2:5 Room3:7 Room4:7
036.Room1:1 Room2:5 Room3:8 Room4:6
037.Room1:1 Room2:5 Room3:9 Room4:5
038.Room1:1 Room2:5 Room3:10 Room4:4
039.Room1:1 Room2:6 Room3:3 Room4:10
040.Room1:1 Room2:6 Room3:4 Room4:9
041.Room1:1 Room2:6 Room3:5 Room4:8
042.Room1:1 Room2:6 Room3:6 Room4:7
043.Room1:1 Room2:6 Room3:7 Room4:6
044.Room1:1 Room2:6 Room3:8 Room4:5
045.Room1:1 Room2:6 Room3:9 Room4:4
046.Room1:1 Room2:7 Room3:3 Room4:9
047.Room1:1 Room2:7 Room3:4 Room4:8
048.Room1:1 Room2:7 Room3:5 Room4:7
049.Room1:1 Room2:7 Room3:6 Room4:6
050.Room1:1 Room2:7 Room3:7 Room4:5
051.Room1:1 Room2:7 Room3:8 Room4:4
052.Room1:1 Room2:8 Room3:3 Room4:8
053.Room1:1 Room2:8 Room3:4 Room4:7
054.Room1:1 Room2:8 Room3:5 Room4:6
055.Room1:1 Room2:8 Room3:6 Room4:5
056.Room1:1 Room2:8 Room3:7 Room4:4
057.Room1:1 Room2:9 Room3:3 Room4:7
058.Room1:1 Room2:9 Room3:4 Room4:6
059.Room1:1 Room2:9 Room3:5 Room4:5
060.Room1:1 Room2:9 Room3:6 Room4:4
061.Room1:1 Room2:10 Room3:3 Room4:6
062.Room1:1 Room2:10 Room3:4 Room4:5
063.Room1:1 Room2:10 Room3:5 Room4:4
064.Room1:1 Room2:11 Room3:3 Room4:5
065.Room1:1 Room2:11 Room3:4 Room4:4
066.Room1:1 Room2:12 Room3:3 Room4:4
067.Room1:2 Room2:2 Room3:3 Room4:13
068.Room1:2 Room2:2 Room3:4 Room4:12
069.Room1:2 Room2:2 Room3:5 Room4:11
070.Room1:2 Room2:2 Room3:6 Room4:10
071.Room1:2 Room2:2 Room3:7 Room4:9
072.Room1:2 Room2:2 Room3:8 Room4:8
073.Room1:2 Room2:2 Room3:9 Room4:7
074.Room1:2 Room2:2 Room3:10 Room4:6
075.Room1:2 Room2:2 Room3:11 Room4:5
076.Room1:2 Room2:2 Room3:12 Room4:4
077.Room1:2 Room2:3 Room3:3 Room4:12
078.Room1:2 Room2:3 Room3:4 Room4:11
079.Room1:2 Room2:3 Room3:5 Room4:10
080.Room1:2 Room2:3 Room3:6 Room4:9
081.Room1:2 Room2:3 Room3:7 Room4:8
082.Room1:2 Room2:3 Room3:8 Room4:7
083.Room1:2 Room2:3 Room3:9 Room4:6
084.Room1:2 Room2:3 Room3:10 Room4:5
085.Room1:2 Room2:3 Room3:11 Room4:4
086.Room1:2 Room2:4 Room3:3 Room4:11
087.Room1:2 Room2:4 Room3:4 Room4:10
088.Room1:2 Room2:4 Room3:5 Room4:9
089.Room1:2 Room2:4 Room3:6 Room4:8
090.Room1:2 Room2:4 Room3:7 Room4:7
091.Room1:2 Room2:4 Room3:8 Room4:6
092.Room1:2 Room2:4 Room3:9 Room4:5
093.Room1:2 Room2:4 Room3:10 Room4:4
094.Room1:2 Room2:5 Room3:3 Room4:10
095.Room1:2 Room2:5 Room3:4 Room4:9
096.Room1:2 Room2:5 Room3:5 Room4:8
097.Room1:2 Room2:5 Room3:6 Room4:7
098.Room1:2 Room2:5 Room3:7 Room4:6
099.Room1:2 Room2:5 Room3:8 Room4:5
100.Room1:2 Room2:5 Room3:9 Room4:4
101.Room1:2 Room2:6 Room3:3 Room4:9
102.Room1:2 Room2:6 Room3:4 Room4:8
103.Room1:2 Room2:6 Room3:5 Room4:7
104.Room1:2 Room2:6 Room3:6 Room4:6
105.Room1:2 Room2:6 Room3:7 Room4:5
106.Room1:2 Room2:6 Room3:8 Room4:4
107.Room1:2 Room2:7 Room3:3 Room4:8
108.Room1:2 Room2:7 Room3:4 Room4:7
109.Room1:2 Room2:7 Room3:5 Room4:6
110.Room1:2 Room2:7 Room3:6 Room4:5
111.Room1:2 Room2:7 Room3:7 Room4:4
112.Room1:2 Room2:8 Room3:3 Room4:7
113.Room1:2 Room2:8 Room3:4 Room4:6
114.Room1:2 Room2:8 Room3:5 Room4:5
115.Room1:2 Room2:8 Room3:6 Room4:4
116.Room1:2 Room2:9 Room3:3 Room4:6
117.Room1:2 Room2:9 Room3:4 Room4:5
118.Room1:2 Room2:9 Room3:5 Room4:4
119.Room1:2 Room2:10 Room3:3 Room4:5
120.Room1:2 Room2:10 Room3:4 Room4:4
121.Room1:2 Room2:11 Room3:3 Room4:4
122.Room1:3 Room2:2 Room3:3 Room4:12
123.Room1:3 Room2:2 Room3:4 Room4:11
124.Room1:3 Room2:2 Room3:5 Room4:10
125.Room1:3 Room2:2 Room3:6 Room4:9
126.Room1:3 Room2:2 Room3:7 Room4:8
127.Room1:3 Room2:2 Room3:8 Room4:7
128.Room1:3 Room2:2 Room3:9 Room4:6
129.Room1:3 Room2:2 Room3:10 Room4:5
130.Room1:3 Room2:2 Room3:11 Room4:4
131.Room1:3 Room2:3 Room3:3 Room4:11
132.Room1:3 Room2:3 Room3:4 Room4:10
133.Room1:3 Room2:3 Room3:5 Room4:9
134.Room1:3 Room2:3 Room3:6 Room4:8
135.Room1:3 Room2:3 Room3:7 Room4:7
136.Room1:3 Room2:3 Room3:8 Room4:6
137.Room1:3 Room2:3 Room3:9 Room4:5
138.Room1:3 Room2:3 Room3:10 Room4:4
139.Room1:3 Room2:4 Room3:3 Room4:10
140.Room1:3 Room2:4 Room3:4 Room4:9
141.Room1:3 Room2:4 Room3:5 Room4:8
142.Room1:3 Room2:4 Room3:6 Room4:7
143.Room1:3 Room2:4 Room3:7 Room4:6
144.Room1:3 Room2:4 Room3:8 Room4:5
145.Room1:3 Room2:4 Room3:9 Room4:4
146.Room1:3 Room2:5 Room3:3 Room4:9
147.Room1:3 Room2:5 Room3:4 Room4:8
148.Room1:3 Room2:5 Room3:5 Room4:7
149.Room1:3 Room2:5 Room3:6 Room4:6
150.Room1:3 Room2:5 Room3:7 Room4:5
151.Room1:3 Room2:5 Room3:8 Room4:4
152.Room1:3 Room2:6 Room3:3 Room4:8
153.Room1:3 Room2:6 Room3:4 Room4:7
154.Room1:3 Room2:6 Room3:5 Room4:6
155.Room1:3 Room2:6 Room3:6 Room4:5
156.Room1:3 Room2:6 Room3:7 Room4:4
157.Room1:3 Room2:7 Room3:3 Room4:7
158.Room1:3 Room2:7 Room3:4 Room4:6
159.Room1:3 Room2:7 Room3:5 Room4:5
160.Room1:3 Room2:7 Room3:6 Room4:4
161.Room1:3 Room2:8 Room3:3 Room4:6
162.Room1:3 Room2:8 Room3:4 Room4:5
163.Room1:3 Room2:8 Room3:5 Room4:4
164.Room1:3 Room2:9 Room3:3 Room4:5
165.Room1:3 Room2:9 Room3:4 Room4:4
166.Room1:3 Room2:10 Room3:3 Room4:4
167.Room1:4 Room2:2 Room3:3 Room4:11
168.Room1:4 Room2:2 Room3:4 Room4:10
169.Room1:4 Room2:2 Room3:5 Room4:9
170.Room1:4 Room2:2 Room3:6 Room4:8
171.Room1:4 Room2:2 Room3:7 Room4:7
172.Room1:4 Room2:2 Room3:8 Room4:6
173.Room1:4 Room2:2 Room3:9 Room4:5
174.Room1:4 Room2:2 Room3:10 Room4:4
175.Room1:4 Room2:3 Room3:3 Room4:10
176.Room1:4 Room2:3 Room3:4 Room4:9
177.Room1:4 Room2:3 Room3:5 Room4:8
178.Room1:4 Room2:3 Room3:6 Room4:7
179.Room1:4 Room2:3 Room3:7 Room4:6
180.Room1:4 Room2:3 Room3:8 Room4:5
181.Room1:4 Room2:3 Room3:9 Room4:4
182.Room1:4 Room2:4 Room3:3 Room4:9
183.Room1:4 Room2:4 Room3:4 Room4:8
184.Room1:4 Room2:4 Room3:5 Room4:7
185.Room1:4 Room2:4 Room3:6 Room4:6
186.Room1:4 Room2:4 Room3:7 Room4:5
187.Room1:4 Room2:4 Room3:8 Room4:4
188.Room1:4 Room2:5 Room3:3 Room4:8
189.Room1:4 Room2:5 Room3:4 Room4:7
190.Room1:4 Room2:5 Room3:5 Room4:6
191.Room1:4 Room2:5 Room3:6 Room4:5
192.Room1:4 Room2:5 Room3:7 Room4:4
193.Room1:4 Room2:6 Room3:3 Room4:7
194.Room1:4 Room2:6 Room3:4 Room4:6
195.Room1:4 Room2:6 Room3:5 Room4:5
196.Room1:4 Room2:6 Room3:6 Room4:4
197.Room1:4 Room2:7 Room3:3 Room4:6
198.Room1:4 Room2:7 Room3:4 Room4:5
199.Room1:4 Room2:7 Room3:5 Room4:4
200.Room1:4 Room2:8 Room3:3 Room4:5
201.Room1:4 Room2:8 Room3:4 Room4:4
202.Room1:4 Room2:9 Room3:3 Room4:4
203.Room1:5 Room2:2 Room3:3 Room4:10
204.Room1:5 Room2:2 Room3:4 Room4:9
205.Room1:5 Room2:2 Room3:5 Room4:8
206.Room1:5 Room2:2 Room3:6 Room4:7
207.Room1:5 Room2:2 Room3:7 Room4:6
208.Room1:5 Room2:2 Room3:8 Room4:5
209.Room1:5 Room2:2 Room3:9 Room4:4
210.Room1:5 Room2:3 Room3:3 Room4:9
211.Room1:5 Room2:3 Room3:4 Room4:8
212.Room1:5 Room2:3 Room3:5 Room4:7
213.Room1:5 Room2:3 Room3:6 Room4:6
214.Room1:5 Room2:3 Room3:7 Room4:5
215.Room1:5 Room2:3 Room3:8 Room4:4
216.Room1:5 Room2:4 Room3:3 Room4:8
217.Room1:5 Room2:4 Room3:4 Room4:7
218.Room1:5 Room2:4 Room3:5 Room4:6
219.Room1:5 Room2:4 Room3:6 Room4:5
220.Room1:5 Room2:4 Room3:7 Room4:4
221.Room1:5 Room2:5 Room3:3 Room4:7
222.Room1:5 Room2:5 Room3:4 Room4:6
223.Room1:5 Room2:5 Room3:5 Room4:5
224.Room1:5 Room2:5 Room3:6 Room4:4
225.Room1:5 Room2:6 Room3:3 Room4:6
226.Room1:5 Room2:6 Room3:4 Room4:5
227.Room1:5 Room2:6 Room3:5 Room4:4
228.Room1:5 Room2:7 Room3:3 Room4:5
229.Room1:5 Room2:7 Room3:4 Room4:4
230.Room1:5 Room2:8 Room3:3 Room4:4
231.Room1:6 Room2:2 Room3:3 Room4:9
232.Room1:6 Room2:2 Room3:4 Room4:8
233.Room1:6 Room2:2 Room3:5 Room4:7
234.Room1:6 Room2:2 Room3:6 Room4:6
235.Room1:6 Room2:2 Room3:7 Room4:5
236.Room1:6 Room2:2 Room3:8 Room4:4
237.Room1:6 Room2:3 Room3:3 Room4:8
238.Room1:6 Room2:3 Room3:4 Room4:7
239.Room1:6 Room2:3 Room3:5 Room4:6
240.Room1:6 Room2:3 Room3:6 Room4:5
241.Room1:6 Room2:3 Room3:7 Room4:4
242.Room1:6 Room2:4 Room3:3 Room4:7
243.Room1:6 Room2:4 Room3:4 Room4:6
244.Room1:6 Room2:4 Room3:5 Room4:5
245.Room1:6 Room2:4 Room3:6 Room4:4
246.Room1:6 Room2:5 Room3:3 Room4:6
247.Room1:6 Room2:5 Room3:4 Room4:5
248.Room1:6 Room2:5 Room3:5 Room4:4
249.Room1:6 Room2:6 Room3:3 Room4:5
250.Room1:6 Room2:6 Room3:4 Room4:4
251.Room1:6 Room2:7 Room3:3 Room4:4
252.Room1:7 Room2:2 Room3:3 Room4:8
253.Room1:7 Room2:2 Room3:4 Room4:7
254.Room1:7 Room2:2 Room3:5 Room4:6
255.Room1:7 Room2:2 Room3:6 Room4:5
256.Room1:7 Room2:2 Room3:7 Room4:4
257.Room1:7 Room2:3 Room3:3 Room4:7
258.Room1:7 Room2:3 Room3:4 Room4:6
259.Room1:7 Room2:3 Room3:5 Room4:5
260.Room1:7 Room2:3 Room3:6 Room4:4
261.Room1:7 Room2:4 Room3:3 Room4:6
262.Room1:7 Room2:4 Room3:4 Room4:5
263.Room1:7 Room2:4 Room3:5 Room4:4
264.Room1:7 Room2:5 Room3:3 Room4:5
265.Room1:7 Room2:5 Room3:4 Room4:4
266.Room1:7 Room2:6 Room3:3 Room4:4
267.Room1:8 Room2:2 Room3:3 Room4:7
268.Room1:8 Room2:2 Room3:4 Room4:6
269.Room1:8 Room2:2 Room3:5 Room4:5
270.Room1:8 Room2:2 Room3:6 Room4:4
271.Room1:8 Room2:3 Room3:3 Room4:6
272.Room1:8 Room2:3 Room3:4 Room4:5
273.Room1:8 Room2:3 Room3:5 Room4:4
274.Room1:8 Room2:4 Room3:3 Room4:5
275.Room1:8 Room2:4 Room3:4 Room4:4
276.Room1:8 Room2:5 Room3:3 Room4:4
277.Room1:9 Room2:2 Room3:3 Room4:6
278.Room1:9 Room2:2 Room3:4 Room4:5
279.Room1:9 Room2:2 Room3:5 Room4:4
280.Room1:9 Room2:3 Room3:3 Room4:5
281.Room1:9 Room2:3 Room3:4 Room4:4
282.Room1:9 Room2:4 Room3:3 Room4:4
283.Room1:10 Room2:2 Room3:3 Room4:5
284.Room1:10 Room2:2 Room3:4 Room4:4
285.Room1:10 Room2:3 Room3:3 Room4:4
286.Room1:11 Room2:2 Room3:3 Room4:4

END