若每个局域网都要与其他局域网直接通信,那么连接n个局域网需要多少个点到点的广域网?
上述问题可以抽象为如下:
已知平面上共有N个点(N为不小于3的整数),其中任意三点都不在同一直线上,那么连接任意两点,可画多少条线段?
答:N!/[(N-2)!2!]
附,当N = 2 ~1000时的结果列表:
2 | 1 |
3 | 3 |
4 | 6 |
5 | 10 |
6 | 15 |
7 | 21 |
8 | 28 |
9 | 36 |
10 | 45 |
11 | 55 |
12 | 66 |
13 | 78 |
14 | 91 |
15 | 105 |
16 | 120 |
17 | 136 |
18 | 153 |
19 | 171 |
20 | 190 |
21 | 210 |
22 | 231 |
23 | 253 |
24 | 276 |
25 | 300 |
26 | 325 |
27 | 351 |
28 | 378 |
29 | 406 |
30 | 435 |
31 | 465 |
32 | 496 |
33 | 528 |
34 | 561 |
35 | 595 |
36 | 630 |
37 | 666 |
38 | 703 |
39 | 741 |
40 | 780 |
41 | 820 |
42 | 861 |
43 | 903 |
44 | 946 |
45 | 990 |
46 | 1035 |
47 | 1081 |
48 | 1128 |
49 | 1176 |
50 | 1225 |
51 | 1275 |
52 | 1326 |
53 | 1378 |
54 | 1431 |
55 | 1485 |
56 | 1540 |
57 | 1596 |
58 | 1653 |
59 | 1711 |
60 | 1770 |
61 | 1830 |
62 | 1891 |
63 | 1953 |
64 | 2016 |
65 | 2080 |
66 | 2145 |
67 | 2211 |
68 | 2278 |
69 | 2346 |
70 | 2415 |
71 | 2485 |
72 | 2556 |
73 | 2628 |
74 | 2701 |
75 | 2775 |
76 | 2850 |
77 | 2926 |
78 | 3003 |
79 | 3081 |
80 | 3160 |
81 | 3240 |
82 | 3321 |
83 | 3403 |
84 | 3486 |
85 | 3570 |
86 | 3655 |
87 | 3741 |
88 | 3828 |
89 | 3916 |
90 | 4005 |
91 | 4095 |
92 | 4186 |
93 | 4278 |
94 | 4371 |
95 | 4465 |
96 | 4560 |
97 | 4656 |
98 | 4753 |
99 | 4851 |
100 | 4950 |
101 | 5050 |
102 | 5151 |
103 | 5253 |
104 | 5356 |
105 | 5460 |
106 | 5565 |
107 | 5671 |
108 | 5778 |
109 | 5886 |
110 | 5995 |
111 | 6105 |
112 | 6216 |
113 | 6328 |
114 | 6441 |
115 | 6555 |
116 | 6670 |
117 | 6786 |
118 | 6903 |
119 | 7021 |
120 | 7140 |
121 | 7260 |
122 | 7381 |
123 | 7503 |
124 | 7626 |
125 | 7750 |
126 | 7875 |
127 | 8001 |
128 | 8128 |
129 | 8256 |
130 | 8385 |
131 | 8515 |
132 | 8646 |
133 | 8778 |
134 | 8911 |
135 | 9045 |
136 | 9180 |
137 | 9316 |
138 | 9453 |
139 | 9591 |
140 | 9730 |
141 | 9870 |
142 | 10011 |
143 | 10153 |
144 | 10296 |
145 | 10440 |
146 | 10585 |
147 | 10731 |
148 | 10878 |
149 | 11026 |
150 | 11175 |
151 | 11325 |
152 | 11476 |
153 | 11628 |
154 | 11781 |
155 | 11935 |
156 | 12090 |
157 | 12246 |
158 | 12403 |
159 | 12561 |
160 | 12720 |
161 | 12880 |
162 | 13041 |
163 | 13203 |
164 | 13366 |
165 | 13530 |
166 | 13695 |
167 | 13861 |
168 | 14028 |
169 | 14196 |
170 | 14365 |
171 | 14535 |
172 | 14706 |
173 | 14878 |
174 | 15051 |
175 | 15225 |
176 | 15400 |
177 | 15576 |
178 | 15753 |
179 | 15931 |
180 | 16110 |
181 | 16290 |
182 | 16471 |
183 | 16653 |
184 | 16836 |
185 | 17020 |
186 | 17205 |
187 | 17391 |
188 | 17578 |
189 | 17766 |
190 | 17955 |
191 | 18145 |
192 | 18336 |
193 | 18528 |
194 | 18721 |
195 | 18915 |
196 | 19110 |
197 | 19306 |
198 | 19503 |
199 | 19701 |
200 | 19900 |
201 | 20100 |
202 | 20301 |
203 | 20503 |
204 | 20706 |
205 | 20910 |
206 | 21115 |
207 | 21321 |
208 | 21528 |
209 | 21736 |
210 | 21945 |
211 | 22155 |
212 | 22366 |
213 | 22578 |
214 | 22791 |
215 | 23005 |
216 | 23220 |
217 | 23436 |
218 | 23653 |
219 | 23871 |
220 | 24090 |
221 | 24310 |
222 | 24531 |
223 | 24753 |
224 | 24976 |
225 | 25200 |
226 | 25425 |
227 | 25651 |
228 | 25878 |
229 | 26106 |
230 | 26335 |
231 | 26565 |
232 | 26796 |
233 | 27028 |
234 | 27261 |
235 | 27495 |
236 | 27730 |
237 | 27966 |
238 | 28203 |
239 | 28441 |
240 | 28680 |
241 | 28920 |
242 | 29161 |
243 | 29403 |
244 | 29646 |
245 | 29890 |
246 | 30135 |
247 | 30381 |
248 | 30628 |
249 | 30876 |
250 | 31125 |
251 | 31375 |
252 | 31626 |
253 | 31878 |
254 | 32131 |
255 | 32385 |
256 | 32640 |
257 | 32896 |
258 | 33153 |
259 | 33411 |
260 | 33670 |
261 | 33930 |
262 | 34191 |
263 | 34453 |
264 | 34716 |
265 | 34980 |
266 | 35245 |
267 | 35511 |
268 | 35778 |
269 | 36046 |
270 | 36315 |
271 | 36585 |
272 | 36856 |
273 | 37128 |
274 | 37401 |
275 | 37675 |
276 | 37950 |
277 | 38226 |
278 | 38503 |
279 | 38781 |
280 | 39060 |
281 | 39340 |
282 | 39621 |
283 | 39903 |
284 | 40186 |
285 | 40470 |
286 | 40755 |
287 | 41041 |
288 | 41328 |
289 | 41616 |
290 | 41905 |
291 | 42195 |
292 | 42486 |
293 | 42778 |
294 | 43071 |
295 | 43365 |
296 | 43660 |
297 | 43956 |
298 | 44253 |
299 | 44551 |
300 | 44850 |
301 | 45150 |
302 | 45451 |
303 | 45753 |
304 | 46056 |
305 | 46360 |
306 | 46665 |
307 | 46971 |
308 | 47278 |
309 | 47586 |
310 | 47895 |
311 | 48205 |
312 | 48516 |
313 | 48828 |
314 | 49141 |
315 | 49455 |
316 | 49770 |
317 | 50086 |
318 | 50403 |
319 | 50721 |
320 | 51040 |
321 | 51360 |
322 | 51681 |
323 | 52003 |
324 | 52326 |
325 | 52650 |
326 | 52975 |
327 | 53301 |
328 | 53628 |
329 | 53956 |
330 | 54285 |
331 | 54615 |
332 | 54946 |
333 | 55278 |
334 | 55611 |
335 | 55945 |
336 | 56280 |
337 | 56616 |
338 | 56953 |
339 | 57291 |
340 | 57630 |
341 | 57970 |
342 | 58311 |
343 | 58653 |
344 | 58996 |
345 | 59340 |
346 | 59685 |
347 | 60031 |
348 | 60378 |
349 | 60726 |
350 | 61075 |
351 | 61425 |
352 | 61776 |
353 | 62128 |
354 | 62481 |
355 | 62835 |
356 | 63190 |
357 | 63546 |
358 | 63903 |
359 | 64261 |
360 | 64620 |
361 | 64980 |
362 | 65341 |
363 | 65703 |
364 | 66066 |
365 | 66430 |
366 | 66795 |
367 | 67161 |
368 | 67528 |
369 | 67896 |
370 | 68265 |
371 | 68635 |
372 | 69006 |
373 | 69378 |
374 | 69751 |
375 | 70125 |
376 | 70500 |
377 | 70876 |
378 | 71253 |
379 | 71631 |
380 | 72010 |
381 | 72390 |
382 | 72771 |
383 | 73153 |
384 | 73536 |
385 | 73920 |
386 | 74305 |
387 | 74691 |
388 | 75078 |
389 | 75466 |
390 | 75855 |
391 | 76245 |
392 | 76636 |
393 | 77028 |
394 | 77421 |
395 | 77815 |
396 | 78210 |
397 | 78606 |
398 | 79003 |
399 | 79401 |
400 | 79800 |
401 | 80200 |
402 | 80601 |
403 | 81003 |
404 | 81406 |
405 | 81810 |
406 | 82215 |
407 | 82621 |
408 | 83028 |
409 | 83436 |
410 | 83845 |
411 | 84255 |
412 | 84666 |
413 | 85078 |
414 | 85491 |
415 | 85905 |
416 | 86320 |
417 | 86736 |
418 | 87153 |
419 | 87571 |
420 | 87990 |
421 | 88410 |
422 | 88831 |
423 | 89253 |
424 | 89676 |
425 | 90100 |
426 | 90525 |
427 | 90951 |
428 | 91378 |
429 | 91806 |
430 | 92235 |
431 | 92665 |
432 | 93096 |
433 | 93528 |
434 | 93961 |
435 | 94395 |
436 | 94830 |
437 | 95266 |
438 | 95703 |
439 | 96141 |
440 | 96580 |
441 | 97020 |
442 | 97461 |
443 | 97903 |
444 | 98346 |
445 | 98790 |
446 | 99235 |
447 | 99681 |
448 | 100128 |
449 | 100576 |
450 | 101025 |
451 | 101475 |
452 | 101926 |
453 | 102378 |
454 | 102831 |
455 | 103285 |
456 | 103740 |
457 | 104196 |
458 | 104653 |
459 | 105111 |
460 | 105570 |
461 | 106030 |
462 | 106491 |
463 | 106953 |
464 | 107416 |
465 | 107880 |
466 | 108345 |
467 | 108811 |
468 | 109278 |
469 | 109746 |
470 | 110215 |
471 | 110685 |
472 | 111156 |
473 | 111628 |
474 | 112101 |
475 | 112575 |
476 | 113050 |
477 | 113526 |
478 | 114003 |
479 | 114481 |
480 | 114960 |
481 | 115440 |
482 | 115921 |
483 | 116403 |
484 | 116886 |
485 | 117370 |
486 | 117855 |
487 | 118341 |
488 | 118828 |
489 | 119316 |
490 | 119805 |
491 | 120295 |
492 | 120786 |
493 | 121278 |
494 | 121771 |
495 | 122265 |
496 | 122760 |
497 | 123256 |
498 | 123753 |
499 | 124251 |
500 | 124750 |
501 | 125250 |
502 | 125751 |
503 | 126253 |
504 | 126756 |
505 | 127260 |
506 | 127765 |
507 | 128271 |
508 | 128778 |
509 | 129286 |
510 | 129795 |
511 | 130305 |
512 | 130816 |
513 | 131328 |
514 | 131841 |
515 | 132355 |
516 | 132870 |
517 | 133386 |
518 | 133903 |
519 | 134421 |
520 | 134940 |
521 | 135460 |
522 | 135981 |
523 | 136503 |
524 | 137026 |
525 | 137550 |
526 | 138075 |
527 | 138601 |
528 | 139128 |
529 | 139656 |
530 | 140185 |
531 | 140715 |
532 | 141246 |
533 | 141778 |
534 | 142311 |
535 | 142845 |
536 | 143380 |
537 | 143916 |
538 | 144453 |
539 | 144991 |
540 | 145530 |
541 | 146070 |
542 | 146611 |
543 | 147153 |
544 | 147696 |
545 | 148240 |
546 | 148785 |
547 | 149331 |
548 | 149878 |
549 | 150426 |
550 | 150975 |
551 | 151525 |
552 | 152076 |
553 | 152628 |
554 | 153181 |
555 | 153735 |
556 | 154290 |
557 | 154846 |
558 | 155403 |
559 | 155961 |
560 | 156520 |
561 | 157080 |
562 | 157641 |
563 | 158203 |
564 | 158766 |
565 | 159330 |
566 | 159895 |
567 | 160461 |
568 | 161028 |
569 | 161596 |
570 | 162165 |
571 | 162735 |
572 | 163306 |
573 | 163878 |
574 | 164451 |
575 | 165025 |
576 | 165600 |
577 | 166176 |
578 | 166753 |
579 | 167331 |
580 | 167910 |
581 | 168490 |
582 | 169071 |
583 | 169653 |
584 | 170236 |
585 | 170820 |
586 | 171405 |
587 | 171991 |
588 | 172578 |
589 | 173166 |
590 | 173755 |
591 | 174345 |
592 | 174936 |
593 | 175528 |
594 | 176121 |
595 | 176715 |
596 | 177310 |
597 | 177906 |
598 | 178503 |
599 | 179101 |
600 | 179700 |
601 | 180300 |
602 | 180901 |
603 | 181503 |
604 | 182106 |
605 | 182710 |
606 | 183315 |
607 | 183921 |
608 | 184528 |
609 | 185136 |
610 | 185745 |
611 | 186355 |
612 | 186966 |
613 | 187578 |
614 | 188191 |
615 | 188805 |
616 | 189420 |
617 | 190036 |
618 | 190653 |
619 | 191271 |
620 | 191890 |
621 | 192510 |
622 | 193131 |
623 | 193753 |
624 | 194376 |
625 | 195000 |
626 | 195625 |
627 | 196251 |
628 | 196878 |
629 | 197506 |
630 | 198135 |
631 | 198765 |
632 | 199396 |
633 | 200028 |
634 | 200661 |
635 | 201295 |
636 | 201930 |
637 | 202566 |
638 | 203203 |
639 | 203841 |
640 | 204480 |
641 | 205120 |
642 | 205761 |
643 | 206403 |
644 | 207046 |
645 | 207690 |
646 | 208335 |
647 | 208981 |
648 | 209628 |
649 | 210276 |
650 | 210925 |
651 | 211575 |
652 | 212226 |
653 | 212878 |
654 | 213531 |
655 | 214185 |
656 | 214840 |
657 | 215496 |
658 | 216153 |
659 | 216811 |
660 | 217470 |
661 | 218130 |
662 | 218791 |
663 | 219453 |
664 | 220116 |
665 | 220780 |
666 | 221445 |
667 | 222111 |
668 | 222778 |
669 | 223446 |
670 | 224115 |
671 | 224785 |
672 | 225456 |
673 | 226128 |
674 | 226801 |
675 | 227475 |
676 | 228150 |
677 | 228826 |
678 | 229503 |
679 | 230181 |
680 | 230860 |
681 | 231540 |
682 | 232221 |
683 | 232903 |
684 | 233586 |
685 | 234270 |
686 | 234955 |
687 | 235641 |
688 | 236328 |
689 | 237016 |
690 | 237705 |
691 | 238395 |
692 | 239086 |
693 | 239778 |
694 | 240471 |
695 | 241165 |
696 | 241860 |
697 | 242556 |
698 | 243253 |
699 | 243951 |
700 | 244650 |
701 | 245350 |
702 | 246051 |
703 | 246753 |
704 | 247456 |
705 | 248160 |
706 | 248865 |
707 | 249571 |
708 | 250278 |
709 | 250986 |
710 | 251695 |
711 | 252405 |
712 | 253116 |
713 | 253828 |
714 | 254541 |
715 | 255255 |
716 | 255970 |
717 | 256686 |
718 | 257403 |
719 | 258121 |
720 | 258840 |
721 | 259560 |
722 | 260281 |
723 | 261003 |
724 | 261726 |
725 | 262450 |
726 | 263175 |
727 | 263901 |
728 | 264628 |
729 | 265356 |
730 | 266085 |
731 | 266815 |
732 | 267546 |
733 | 268278 |
734 | 269011 |
735 | 269745 |
736 | 270480 |
737 | 271216 |
738 | 271953 |
739 | 272691 |
740 | 273430 |
741 | 274170 |
742 | 274911 |
743 | 275653 |
744 | 276396 |
745 | 277140 |
746 | 277885 |
747 | 278631 |
748 | 279378 |
749 | 280126 |
750 | 280875 |
751 | 281625 |
752 | 282376 |
753 | 283128 |
754 | 283881 |
755 | 284635 |
756 | 285390 |
757 | 286146 |
758 | 286903 |
759 | 287661 |
760 | 288420 |
761 | 289180 |
762 | 289941 |
763 | 290703 |
764 | 291466 |
765 | 292230 |
766 | 292995 |
767 | 293761 |
768 | 294528 |
769 | 295296 |
770 | 296065 |
771 | 296835 |
772 | 297606 |
773 | 298378 |
774 | 299151 |
775 | 299925 |
776 | 300700 |
777 | 301476 |
778 | 302253 |
779 | 303031 |
780 | 303810 |
781 | 304590 |
782 | 305371 |
783 | 306153 |
784 | 306936 |
785 | 307720 |
786 | 308505 |
787 | 309291 |
788 | 310078 |
789 | 310866 |
790 | 311655 |
791 | 312445 |
792 | 313236 |
793 | 314028 |
794 | 314821 |
795 | 315615 |
796 | 316410 |
797 | 317206 |
798 | 318003 |
799 | 318801 |
800 | 319600 |
801 | 320400 |
802 | 321201 |
803 | 322003 |
804 | 322806 |
805 | 323610 |
806 | 324415 |
807 | 325221 |
808 | 326028 |
809 | 326836 |
810 | 327645 |
811 | 328455 |
812 | 329266 |
813 | 330078 |
814 | 330891 |
815 | 331705 |
816 | 332520 |
817 | 333336 |
818 | 334153 |
819 | 334971 |
820 | 335790 |
821 | 336610 |
822 | 337431 |
823 | 338253 |
824 | 339076 |
825 | 339900 |
826 | 340725 |
827 | 341551 |
828 | 342378 |
829 | 343206 |
830 | 344035 |
831 | 344865 |
832 | 345696 |
833 | 346528 |
834 | 347361 |
835 | 348195 |
836 | 349030 |
837 | 349866 |
838 | 350703 |
839 | 351541 |
840 | 352380 |
841 | 353220 |
842 | 354061 |
843 | 354903 |
844 | 355746 |
845 | 356590 |
846 | 357435 |
847 | 358281 |
848 | 359128 |
849 | 359976 |
850 | 360825 |
851 | 361675 |
852 | 362526 |
853 | 363378 |
854 | 364231 |
855 | 365085 |
856 | 365940 |
857 | 366796 |
858 | 367653 |
859 | 368511 |
860 | 369370 |
861 | 370230 |
862 | 371091 |
863 | 371953 |
864 | 372816 |
865 | 373680 |
866 | 374545 |
867 | 375411 |
868 | 376278 |
869 | 377146 |
870 | 378015 |
871 | 378885 |
872 | 379756 |
873 | 380628 |
874 | 381501 |
875 | 382375 |
876 | 383250 |
877 | 384126 |
878 | 385003 |
879 | 385881 |
880 | 386760 |
881 | 387640 |
882 | 388521 |
883 | 389403 |
884 | 390286 |
885 | 391170 |
886 | 392055 |
887 | 392941 |
888 | 393828 |
889 | 394716 |
890 | 395605 |
891 | 396495 |
892 | 397386 |
893 | 398278 |
894 | 399171 |
895 | 400065 |
896 | 400960 |
897 | 401856 |
898 | 402753 |
899 | 403651 |
900 | 404550 |
901 | 405450 |
902 | 406351 |
903 | 407253 |
904 | 408156 |
905 | 409060 |
906 | 409965 |
907 | 410871 |
908 | 411778 |
909 | 412686 |
910 | 413595 |
911 | 414505 |
912 | 415416 |
913 | 416328 |
914 | 417241 |
915 | 418155 |
916 | 419070 |
917 | 419986 |
918 | 420903 |
919 | 421821 |
920 | 422740 |
921 | 423660 |
922 | 424581 |
923 | 425503 |
924 | 426426 |
925 | 427350 |
926 | 428275 |
927 | 429201 |
928 | 430128 |
929 | 431056 |
930 | 431985 |
931 | 432915 |
932 | 433846 |
933 | 434778 |
934 | 435711 |
935 | 436645 |
936 | 437580 |
937 | 438516 |
938 | 439453 |
939 | 440391 |
940 | 441330 |
941 | 442270 |
942 | 443211 |
943 | 444153 |
944 | 445096 |
945 | 446040 |
946 | 446985 |
947 | 447931 |
948 | 448878 |
949 | 449826 |
950 | 450775 |
951 | 451725 |
952 | 452676 |
953 | 453628 |
954 | 454581 |
955 | 455535 |
956 | 456490 |
957 | 457446 |
958 | 458403 |
959 | 459361 |
960 | 460320 |
961 | 461280 |
962 | 462241 |
963 | 463203 |
964 | 464166 |
965 | 465130 |
966 | 466095 |
967 | 467061 |
968 | 468028 |
969 | 468996 |
970 | 469965 |
971 | 470935 |
972 | 471906 |
973 | 472878 |
974 | 473851 |
975 | 474825 |
976 | 475800 |
977 | 476776 |
978 | 477753 |
979 | 478731 |
980 | 479710 |
981 | 480690 |
982 | 481671 |
983 | 482653 |
984 | 483636 |
985 | 484620 |
986 | 485605 |
987 | 486591 |
988 | 487578 |
989 | 488566 |
990 | 489555 |
991 | 490545 |
992 | 491536 |
993 | 492528 |
994 | 493521 |
995 | 494515 |
996 | 495510 |
997 | 496506 |
998 | 497503 |
999 | 498501 |
1000 | 499500 |