puzzleup 2021

newkid

solomon_007 发表于 2021-10-13 21:24
这显然是 4 啊， 在任何一条能容下4个棋子的对角线上，部署4个棋子，就是一个满足条件的答案修正一下，先去 ...

你这个N=10答案，如果去掉2,3,5行, 1,4,6列，就变空白了。

solomon_007

newkid 发表于 2021-10-14 22:03
你这个N=10答案，如果去掉2,3,5行, 1,4,6列，就变空白了。

10 的确不行，两条对角线的 12 也可以。

newkid

12就是我昨天说的6,6,2
等会准备写个程序把N=10, 11 暴力跑一下。

newkid

N=10还确实有解。你们也找找看。

dhhb

暴力加模拟抽样，N=10找到几个解,<10的找不到
[{(1, 1),
  (2, 4),
  (3, 3),
  (3, 5),
  (4, 2),
  (4, 3),
  (5, 5),
  (5, 6),
  (6, 2),
  (6, 6)},
{(1, 1),
  (1, 3),
  (2, 1),
  (2, 4),
  (3, 2),
  (4, 6),
  (5, 3),
  (5, 5),
  (6, 4),
  (6, 5)},
{(1, 1),
  (1, 3),
  (2, 2),
  (3, 6),
  (4, 3),
  (4, 5),
  (5, 1),
  (5, 4),
  (6, 4),
  (6, 5)}]

newkid

dhhb 发表于 2021-10-15 10:19
暴力加模拟抽样，N=10找到几个解,

答案是对的，你把代码晒一下？
N>9 是可以证明的。如果能用推理的方法弄出一个N=10的答案就更厉害了。

dhhb

newkid 发表于 2021-10-15 21:22
答案是对的，你把代码晒一下？N>9 是可以证明的。如果能用推理的方法弄出一个N=10的答案就更厉害了。

sql我写不出来，就用过程，我先说说思路, 就是一共有C6,3 * C6,3种划分方法，对每一个方法划分后剩余的9个点作为一个集合，这样一共收集到400个唯一的集合。 然后建立空集合S, 从第一个集合开始，随机取一个点A，加入S, 接下来看第二个集合，如果A存在第二个集合，那么就表示A可以在第一或第二两个方法划分后存在，此时不用考虑第二集合，直接跳到第三集合。如果A不存在第二集合，那么在第二集合再随机取点B. 这样AB都加入S. 依次再处理第三直到最后，每次处理的集合如果和S没有交集，就加入一个点。 400个处理完成后输出S就是所选择的点。 因为是随机取的，循环10000次，就能得到10个的方法。

〇〇

好办法

〇〇

正向试探是否可行，把400个3x3集合从左上先右后下依次计算交集，比如前2个交集是2-3列的1-3行，这6个格必填其中一个

solomon_007

1        2,3,7,8,13,16,21,22,29,36
2        2,3,7,8,13,16,21,22,30,35
3        2,3,7,8,13,16,23,27,28,36
4        2,3,7,8,13,16,23,30,33,34
5        2,3,7,8,13,16,24,27,28,35
6        2,3,7,8,13,16,24,29,33,34
7        2,3,7,8,13,17,21,23,28,36
8        2,3,7,8,13,17,21,23,30,34
9        2,3,7,8,13,17,22,27,29,36
10        2,3,7,8,13,17,22,30,33,35
11        2,3,7,8,13,17,24,27,29,34
12        2,3,7,8,13,17,24,28,33,35
13        2,3,7,8,13,18,21,24,28,35
14        2,3,7,8,13,18,21,24,29,34
15        2,3,7,8,13,18,22,27,30,35
16        2,3,7,8,13,18,22,29,33,36
17        2,3,7,8,13,18,23,27,30,34
18        2,3,7,8,13,18,23,28,33,36
19        2,3,7,8,15,16,19,22,29,36
20        2,3,7,8,15,16,19,22,30,35
21        2,3,7,8,15,16,23,25,28,36
22        2,3,7,8,15,16,23,30,31,34
23        2,3,7,8,15,16,24,25,28,35
24        2,3,7,8,15,16,24,29,31,34
25        2,3,7,8,15,17,19,23,28,36
26        2,3,7,8,15,17,19,23,30,34
27        2,3,7,8,15,17,22,25,29,36
28        2,3,7,8,15,17,22,30,31,35
29        2,3,7,8,15,17,24,25,29,34
30        2,3,7,8,15,17,24,28,31,35
31        2,3,7,8,15,18,19,24,28,35
32        2,3,7,8,15,18,19,24,29,34
33        2,3,7,8,15,18,22,25,30,35
34        2,3,7,8,15,18,22,29,31,36
35        2,3,7,8,15,18,23,25,30,34
36        2,3,7,8,15,18,23,28,31,36
37        2,3,7,8,16,19,23,27,29,36
38        2,3,7,8,16,19,23,30,33,35
39        2,3,7,8,16,19,24,27,30,35
40        2,3,7,8,16,19,24,29,33,36
41        2,3,7,8,16,21,23,25,29,36
42        2,3,7,8,16,21,23,30,31,35
43        2,3,7,8,16,21,24,25,30,35
44        2,3,7,8,16,21,24,29,31,36
45        2,3,7,8,16,23,25,30,33,36
46        2,3,7,8,16,23,27,30,31,36
47        2,3,7,8,16,24,25,29,33,35
48        2,3,7,8,16,24,27,29,31,35
49        2,3,7,8,17,19,22,27,28,36
50        2,3,7,8,17,19,22,30,33,34
51        2,3,7,8,17,19,24,27,30,34
52        2,3,7,8,17,19,24,28,33,36
53        2,3,7,8,17,21,22,25,28,36
54        2,3,7,8,17,21,22,30,31,34
55        2,3,7,8,17,21,24,25,30,34
56        2,3,7,8,17,21,24,28,31,36
57        2,3,7,8,17,22,25,30,33,36
58        2,3,7,8,17,22,27,30,31,36
59        2,3,7,8,17,24,25,28,33,34
60        2,3,7,8,17,24,27,28,31,34
61        2,3,7,8,18,19,22,27,28,35
62        2,3,7,8,18,19,22,29,33,34
63        2,3,7,8,18,19,23,27,29,34
64        2,3,7,8,18,19,23,28,33,35
65        2,3,7,8,18,21,22,25,28,35
66        2,3,7,8,18,21,22,29,31,34
67        2,3,7,8,18,21,23,25,29,34
68        2,3,7,8,18,21,23,28,31,35
69        2,3,7,8,18,22,25,29,33,35
70        2,3,7,8,18,22,27,29,31,35
71        2,3,7,8,18,23,25,28,33,34
72        2,3,7,8,18,23,27,28,31,34
73        2,3,7,9,13,16,20,22,29,36
74        2,3,7,9,13,16,20,22,30,35
75        2,3,7,9,13,16,23,26,28,36
76        2,3,7,9,13,16,23,30,32,34
77        2,3,7,9,13,16,24,26,28,35
78        2,3,7,9,13,16,24,29,32,34
79        2,3,7,9,13,17,20,23,28,36
80        2,3,7,9,13,17,20,23,30,34
81        2,3,7,9,13,17,22,26,29,36
82        2,3,7,9,13,17,22,30,32,35
83        2,3,7,9,13,17,24,26,29,34
84        2,3,7,9,13,17,24,28,32,35
85        2,3,7,9,13,18,20,24,28,35
86        2,3,7,9,13,18,20,24,29,34
87        2,3,7,9,13,18,22,26,30,35
88        2,3,7,9,13,18,22,29,32,36
89        2,3,7,9,13,18,23,26,30,34
90        2,3,7,9,13,18,23,28,32,36
91        2,3,7,9,14,16,19,22,29,36
92        2,3,7,9,14,16,19,22,30,35
93        2,3,7,9,14,16,23,25,28,36
94        2,3,7,9,14,16,23,30,31,34
95        2,3,7,9,14,16,24,25,28,35
96        2,3,7,9,14,16,24,29,31,34
97        2,3,7,9,14,17,19,23,28,36
98        2,3,7,9,14,17,19,23,30,34
99        2,3,7,9,14,17,22,25,29,36
100        2,3,7,9,14,17,22,30,31,35
**        2,3,7,9,14,17,24,25,29,34
102        2,3,7,9,14,17,24,28,31,35
103        2,3,7,9,14,18,19,24,28,35
104        2,3,7,9,14,18,19,24,29,34
105        2,3,7,9,14,18,22,25,30,35
106        2,3,7,9,14,18,22,29,31,36
107        2,3,7,9,14,18,23,25,30,34
108        2,3,7,9,14,18,23,28,31,36
109        2,3,7,9,16,19,23,26,29,36
110        2,3,7,9,16,19,23,30,32,35
111        2,3,7,9,16,19,24,26,30,35
112        2,3,7,9,16,19,24,29,32,36
113        2,3,7,9,16,20,23,25,29,36
114        2,3,7,9,16,20,23,30,31,35
115        2,3,7,9,16,20,24,25,30,35
116        2,3,7,9,16,20,24,29,31,36
117        2,3,7,9,16,23,25,30,32,36
118        2,3,7,9,16,23,26,30,31,36
119        2,3,7,9,16,24,25,29,32,35
120        2,3,7,9,16,24,26,29,31,35
121        2,3,7,9,17,19,22,26,28,36
122        2,3,7,9,17,19,22,30,32,34
123        2,3,7,9,17,19,24,26,30,34
124        2,3,7,9,17,19,24,28,32,36
125        2,3,7,9,17,20,22,25,28,36
126        2,3,7,9,17,20,22,30,31,34
127        2,3,7,9,17,20,24,25,30,34
128        2,3,7,9,17,20,24,28,31,36
129        2,3,7,9,17,22,25,30,32,36
130        2,3,7,9,17,22,26,30,31,36
131        2,3,7,9,17,24,25,28,32,34
132        2,3,7,9,17,24,26,28,31,34
133        2,3,7,9,18,19,22,26,28,35
134        2,3,7,9,18,19,22,29,32,34
135        2,3,7,9,18,19,23,26,29,34
136        2,3,7,9,18,19,23,28,32,35
137        2,3,7,9,18,20,22,25,28,35
138        2,3,7,9,18,20,22,29,31,34
139        2,3,7,9,18,20,23,25,29,34
140        2,3,7,9,18,20,23,28,31,35
141        2,3,7,9,18,22,25,29,32,35
142        2,3,7,9,18,22,26,29,31,35
143        2,3,7,9,18,23,25,28,32,34
144        2,3,7,9,18,23,26,28,31,34
145        2,3,7,10,13,14,21,22,29,36
146        2,3,7,10,13,14,21,22,30,35
147        2,3,7,10,13,14,23,27,28,36
148        2,3,7,10,13,14,23,30,33,34
149        2,3,7,10,13,14,24,27,28,35
150        2,3,7,10,13,14,24,29,33,34
151        2,3,7,10,13,15,20,22,29,36
152        2,3,7,10,13,15,20,22,30,35
153        2,3,7,10,13,15,23,26,28,36
154        2,3,7,10,13,15,23,30,32,34
155        2,3,7,10,13,15,24,26,28,35
156        2,3,7,10,13,15,24,29,32,34
157        2,3,7,10,14,16,19,21,29,36
158        2,3,7,10,14,16,19,21,30,35
159        2,3,7,10,14,16,23,25,27,36
160        2,3,7,10,14,16,23,30,31,33
161        2,3,7,10,14,16,24,25,27,35
162        2,3,7,10,14,16,24,29,31,33
163        2,3,7,10,15,16,19,20,29,36
164        2,3,7,10,15,16,19,20,30,35
165        2,3,7,10,15,16,23,25,26,36
166        2,3,7,10,15,16,23,30,31,32
167        2,3,7,10,15,16,24,25,26,35
168        2,3,7,10,15,16,24,29,31,32
169        2,3,7,10,17,19,20,27,28,36
170        2,3,7,10,17,19,20,30,33,34
171        2,3,7,10,17,19,21,26,28,36
172        2,3,7,10,17,19,21,30,32,34
173        2,3,7,10,17,20,22,25,27,36
174        2,3,7,10,17,20,22,30,31,33
175        2,3,7,10,17,21,22,25,26,36
176        2,3,7,10,17,21,22,30,31,32
177        2,3,7,10,17,24,25,26,33,34
178        2,3,7,10,17,24,25,27,32,34
179        2,3,7,10,17,24,26,28,31,33
180        2,3,7,10,17,24,27,28,31,32
181        2,3,7,10,18,19,20,27,28,35
182        2,3,7,10,18,19,20,29,33,34
183        2,3,7,10,18,19,21,26,28,35
184        2,3,7,10,18,19,21,29,32,34
185        2,3,7,10,18,20,22,25,27,35
186        2,3,7,10,18,20,22,29,31,33
187        2,3,7,10,18,21,22,25,26,35
188        2,3,7,10,18,21,22,29,31,32
189        2,3,7,10,18,23,25,26,33,34
190        2,3,7,10,18,23,25,27,32,34
191        2,3,7,10,18,23,26,28,31,33
192        2,3,7,10,18,23,27,28,31,32
193        2,3,7,11,13,14,21,23,28,36
194        2,3,7,11,13,14,21,23,30,34
195        2,3,7,11,13,14,22,27,29,36
196        2,3,7,11,13,14,22,30,33,35
197        2,3,7,11,13,14,24,27,29,34
198        2,3,7,11,13,14,24,28,33,35
199        2,3,7,11,13,15,20,23,28,36
200        2,3,7,11,13,15,20,23,30,34
201        2,3,7,11,13,15,22,26,29,36
202        2,3,7,11,13,15,22,30,32,35
203        2,3,7,11,13,15,24,26,29,34
204        2,3,7,11,13,15,24,28,32,35
205        2,3,7,11,14,17,19,21,28,36
206        2,3,7,11,14,17,19,21,30,34
207        2,3,7,11,14,17,22,25,27,36
208        2,3,7,11,14,17,22,30,31,33
209        2,3,7,11,14,17,24,25,27,34
210        2,3,7,11,14,17,24,28,31,33
211        2,3,7,11,15,17,19,20,28,36
212        2,3,7,11,15,17,19,20,30,34
213        2,3,7,11,15,17,22,25,26,36
214        2,3,7,11,15,17,22,30,31,32
215        2,3,7,11,15,17,24,25,26,34
216        2,3,7,11,15,17,24,28,31,32
217        2,3,7,11,16,19,20,27,29,36
218        2,3,7,11,16,19,20,30,33,35
219        2,3,7,11,16,19,21,26,29,36
220        2,3,7,11,16,19,21,30,32,35
221        2,3,7,11,16,20,23,25,27,36
222        2,3,7,11,16,20,23,30,31,33
223        2,3,7,11,16,21,23,25,26,36
224        2,3,7,11,16,21,23,30,31,32
225        2,3,7,11,16,24,25,26,33,35
226        2,3,7,11,16,24,25,27,32,35
227        2,3,7,11,16,24,26,29,31,33
228        2,3,7,11,16,24,27,29,31,32
229        2,3,7,11,18,19,20,27,29,34
230        2,3,7,11,18,19,20,28,33,35
231        2,3,7,11,18,19,21,26,29,34
232        2,3,7,11,18,19,21,28,32,35
233        2,3,7,11,18,20,23,25,27,34
234        2,3,7,11,18,20,23,28,31,33
235        2,3,7,11,18,21,23,25,26,34
236        2,3,7,11,18,21,23,28,31,32
237        2,3,7,11,18,22,25,26,33,35
238        2,3,7,11,18,22,25,27,32,35
239        2,3,7,11,18,22,26,29,31,33
240        2,3,7,11,18,22,27,29,31,32
241        2,3,7,12,13,14,21,24,28,35
242        2,3,7,12,13,14,21,24,29,34
243        2,3,7,12,13,14,22,27,30,35
244        2,3,7,12,13,14,22,29,33,36
245        2,3,7,12,13,14,23,27,30,34
246        2,3,7,12,13,14,23,28,33,36
247        2,3,7,12,13,15,20,24,28,35
248        2,3,7,12,13,15,20,24,29,34
249        2,3,7,12,13,15,22,26,30,35
250        2,3,7,12,13,15,22,29,32,36
251        2,3,7,12,13,15,23,26,30,34
252        2,3,7,12,13,15,23,28,32,36
253        2,3,7,12,14,18,19,21,28,35
254        2,3,7,12,14,18,19,21,29,34
255        2,3,7,12,14,18,22,25,27,35
256        2,3,7,12,14,18,22,29,31,33
257        2,3,7,12,14,18,23,25,27,34
258        2,3,7,12,14,18,23,28,31,33
259        2,3,7,12,15,18,19,20,28,35
260        2,3,7,12,15,18,19,20,29,34
261        2,3,7,12,15,18,22,25,26,35
262        2,3,7,12,15,18,22,29,31,32
263        2,3,7,12,15,18,23,25,26,34
264        2,3,7,12,15,18,23,28,31,32
265        2,3,7,12,16,19,20,27,30,35
266        2,3,7,12,16,19,20,29,33,36
267        2,3,7,12,16,19,21,26,30,35
268        2,3,7,12,16,19,21,29,32,36
269        2,3,7,12,16,20,24,25,27,35
270        2,3,7,12,16,20,24,29,31,33
271        2,3,7,12,16,21,24,25,26,35
272        2,3,7,12,16,21,24,29,31,32
273        2,3,7,12,16,23,25,26,33,36
274        2,3,7,12,16,23,25,27,32,36
275        2,3,7,12,16,23,26,30,31,33
276        2,3,7,12,16,23,27,30,31,32
277        2,3,7,12,17,19,20,27,30,34
278        2,3,7,12,17,19,20,28,33,36
279        2,3,7,12,17,19,21,26,30,34
280        2,3,7,12,17,19,21,28,32,36
281        2,3,7,12,17,20,24,25,27,34
282        2,3,7,12,17,20,24,28,31,33
283        2,3,7,12,17,21,24,25,26,34
284        2,3,7,12,17,21,24,28,31,32
285        2,3,7,12,17,22,25,26,33,36
286        2,3,7,12,17,22,25,27,32,36
287        2,3,7,12,17,22,26,30,31,33
288        2,3,7,12,17,22,27,30,31,32
289        2,3,7,14,16,21,23,28,29,36
290        2,3,7,14,16,21,23,30,34,35
291        2,3,7,14,16,21,24,28,30,35
292        2,3,7,14,16,21,24,29,34,36
293        2,3,7,14,16,22,23,27,29,36
294        2,3,7,14,16,22,23,30,33,35
295        2,3,7,14,16,22,24,27,30,35
296        2,3,7,14,16,22,24,29,33,36
297        2,3,7,14,16,23,27,30,34,36
298        2,3,7,14,16,23,28,30,33,36
299        2,3,7,14,16,24,27,29,34,35
300        2,3,7,14,16,24,28,29,33,35
301        2,3,7,14,17,21,22,28,29,36
302        2,3,7,14,17,21,22,30,34,35
303        2,3,7,14,17,21,24,28,35,36
304        2,3,7,14,17,21,24,29,30,34
305        2,3,7,14,17,22,23,27,28,36
306        2,3,7,14,17,22,23,30,33,34
307        2,3,7,14,17,22,27,30,35,36
308        2,3,7,14,17,22,29,30,33,36
309        2,3,7,14,17,23,24,27,30,34
310        2,3,7,14,17,23,24,28,33,36
311        2,3,7,14,17,24,27,28,34,35
312        2,3,7,14,17,24,28,29,33,34
313        2,3,7,14,18,21,22,28,30,35
314        2,3,7,14,18,21,22,29,34,36
315        2,3,7,14,18,21,23,28,35,36
316        2,3,7,14,18,21,23,29,30,34
317        2,3,7,14,18,22,24,27,28,35
318        2,3,7,14,18,22,24,29,33,34
319        2,3,7,14,18,22,27,29,35,36
320        2,3,7,14,18,22,29,30,33,35
321        2,3,7,14,18,23,24,27,29,34
322        2,3,7,14,18,23,24,28,33,35
323        2,3,7,14,18,23,27,28,34,36
324        2,3,7,14,18,23,28,30,33,34
325        2,3,7,15,16,20,23,28,29,36
326        2,3,7,15,16,20,23,30,34,35
327        2,3,7,15,16,20,24,28,30,35
328        2,3,7,15,16,20,24,29,34,36
329        2,3,7,15,16,22,23,26,29,36
330        2,3,7,15,16,22,23,30,32,35
331        2,3,7,15,16,22,24,26,30,35
332        2,3,7,15,16,22,24,29,32,36
333        2,3,7,15,16,23,26,30,34,36
334        2,3,7,15,16,23,28,30,32,36
335        2,3,7,15,16,24,26,29,34,35
336        2,3,7,15,16,24,28,29,32,35
337        2,3,7,15,17,20,22,28,29,36
338        2,3,7,15,17,20,22,30,34,35
339        2,3,7,15,17,20,24,28,35,36
340        2,3,7,15,17,20,24,29,30,34
341        2,3,7,15,17,22,23,26,28,36
342        2,3,7,15,17,22,23,30,32,34
343        2,3,7,15,17,22,26,30,35,36
......