人数VS誕生日が同じペア(組):うるう年ありバージョン

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はじめに

※追記:完成したアプリの紹介→同じ誕生日のペアがどのくらいいるかシミュレーション

誕生日の組を求めるプログラム (c++/c言語)で誕生日のペアを求めるプログラムを紹介した。

多くの人は、わざわざこのプログラムを自分で動かしたいと思う人は多くはいないだろう。

それよりも、過程はどうでもいいからとっとと結果を教えてほしい人の方が多いと思われる。

以下では、うるう年を含めた(最大366ペア)のシミュレーション結果を示したいと思う。

※あくまで、この結果はシミュレーション。厳密な答えではない。まれに、人数が増えていても、誕生日が同じペア(期待値)が減っていることがある

※人数VS誕生日が同じペア(うるう年なしバージョン)は次の記事を参照:人数VS誕生日が同じペア(組):うるう年なしバージョン

※http://ict119.com/birthday365-table/ ‎使用しているプログラムは、誕生日の組を求めるプログラム (c++/c言語)で紹介した2人~特定の人数までの誕生日の組(期待値)を求める [3ループ](うるう年あり)。条件は試行回数(k_max=100000)100000回(10万回)

※プログラムが終了するのに2時間近くかかった……。

グラフ

Gnuplotという無料のグラフ作成ソフトで作成。

simulation_k100000_366

 

テーブル

エクセルファイル(結果)のダウンロード:simulation_k100000_d366.xlse

 

人数 同じ誕生日のペアの期待値(pair_exp)
2 0.00292
3 0.00867
4 0.01598
5 0.02756
6 0.04096
7 0.05687
8 0.07394
9 0.09761
10 0.12077
11 0.14894
12 0.17625
13 0.20705
14 0.24467
15 0.28195
16 0.32257
17 0.36301
18 0.40543
19 0.45118
20 0.50135
21 0.55373
22 0.61141
23 0.66387
24 0.72641
25 0.7893
26 0.84997
27 0.91502
28 0.99018
29 1.05699
30 1.129
31 1.20377
32 1.28821
33 1.36062
34 1.44464
35 1.53047
36 1.62382
37 1.70364
38 1.80209
39 1.89631
40 1.99319
41 2.09043
42 2.19121
43 2.28964
44 2.40235
45 2.5094
46 2.61608
47 2.72555
48 2.84231
49 2.94678
50 3.07487
51 3.18873
52 3.30593
53 3.43564
54 3.56289
55 3.68433
56 3.81357
57 3.95532
58 4.08005
59 4.21779
60 4.36275
61 4.49392
62 4.64128
63 4.79412
64 4.93502
65 5.07052
66 5.22781
67 5.37617
68 5.52846
69 5.68566
70 5.83965
71 6.00057
72 6.17022
73 6.32027
74 6.4806
75 6.64209
76 6.82155
77 6.9941
78 7.15544
79 7.32673
80 7.51528
81 7.68969
82 7.85341
83 8.04229
84 8.22428
85 8.40831
86 8.59269
87 8.77811
88 8.9587
89 9.1599
90 9.34662
91 9.54499
92 9.74346
93 9.93862
94 10.12533
95 10.31989
96 10.53792
97 10.73111
98 10.9298
99 11.12862
100 11.34775
101 11.55016
102 11.77045
103 11.98678
104 12.20003
105 12.41446
106 12.6079
107 12.84305
108 13.06057
109 13.28015
110 13.49239
111 13.72572
112 13.94437
113 14.15884
114 14.41146
115 14.63561
116 14.85325
117 15.08458
118 15.31877
119 15.5628
120 15.80878
121 16.03015
122 16.26779
123 16.50723
124 16.73127
125 16.99112
126 17.24236
127 17.47382
128 17.73389
129 17.97034
130 18.22965
131 18.47074
132 18.72834
133 18.97018
134 19.21814
135 19.49011
136 19.72511
137 19.99699
138 20.25287
139 20.51821
140 20.7719
141 21.04789
142 21.28745
143 21.56274
144 21.83141
145 22.09896
146 22.37029
147 22.61532
148 22.89868
149 23.16903
150 23.45351
151 23.72597
152 23.97428
153 24.25751
154 24.54504
155 24.83496
156 25.0776
157 25.3788
158 25.66232
159 25.94134
160 26.21517
161 26.50133
162 26.79506
163 27.06816
164 27.3542
165 27.63355
166 27.93178
167 28.22543
168 28.48314
169 28.79333
170 29.09654
171 29.38426
172 29.67324
173 29.97577
174 30.27407
175 30.57463
176 30.85724
177 31.16613
178 31.44618
179 31.7592
180 32.04545
181 32.36445
182 32.66325
183 32.9615
184 33.26652
185 33.57361
186 33.89031
187 34.18527
188 34.50359
189 34.80138
190 35.11408
191 35.42889
192 35.73482
193 36.03315
194 36.35855
195 36.68844
196 36.98795
197 37.28978
198 37.63374
199 37.92021
200 38.23758
201 38.55683
202 38.86387
203 39.21997
204 39.53859
205 39.83323
206 40.17072
207 40.45607
208 40.81578
209 41.13364
210 41.4547
211 41.78819
212 42.10489
213 42.43626
214 42.74988
215 43.07949
216 43.40608
217 43.71614
218 44.06528
219 44.39672
220 44.71587
221 45.05092
222 45.39103
223 45.70235
224 46.03182
225 46.38269
226 46.73803
227 47.02498
228 47.36766
229 47.68963
230 48.03049
231 48.39147
232 48.70238
233 49.04797
234 49.3997
235 49.71916
236 50.06526
237 50.38664
238 50.7307
239 51.10479
240 51.41342
241 51.76781
242 52.12454
243 52.45277
244 52.79693
245 53.14538
246 53.481
247 53.84353
248 54.15924
249 54.50136
250 54.86593
251 55.17845
252 55.5555
253 55.88814
254 56.21794
255 56.60546
256 56.95352
257 57.28496
258 57.62141
259 57.98925
260 58.34548
261 58.68261
262 59.04727
263 59.37953
264 59.73587
265 60.09456
266 60.45153
267 60.79436
268 61.15972
269 61.47013
270 61.85504
271 62.20372
272 62.55129
273 62.90081
274 63.26884
275 63.6059
276 63.97243
277 64.33565
278 64.68186
279 65.06329
280 65.40173
281 65.76275
282 66.11437
283 66.44356
284 66.82161
285 67.21621
286 67.52418
287 67.91051
288 68.27705
289 68.61931
290 68.99511
291 69.34208
292 69.71183
293 70.04709
294 70.431
295 70.79582
296 71.14096
297 71.49616
298 71.86588
299 72.22484
300 72.58607
301 72.93998
302 73.29405
303 73.66954
304 74.02237
305 74.3806
306 74.74761
307 75.10354
308 75.49936
309 75.84052
310 76.19371
311 76.56759
312 76.93385
313 77.30287
314 77.65138
315 78.02215
316 78.39857
317 78.76408
318 79.10128
319 79.49899
320 79.86552
321 80.20651
322 80.58493
323 80.93496
324 81.31156
325 81.71613
326 82.03596
327 82.41321
328 82.78174
329 83.14123
330 83.51839
331 83.87344
332 84.25321
333 84.61305
334 84.98136
335 85.34671
336 85.7116
337 86.10308
338 86.44766
339 86.81506
340 87.19032
341 87.55279
342 87.91799
343 88.29112
344 88.65459
345 89.01948
346 89.37291
347 89.74958
348 90.13153
349 90.51228
350 90.86669
351 91.20609
352 91.57867
353 91.99275
354 92.31481
355 92.70782
356 93.06336
357 93.42829
358 93.8076
359 94.17864
360 94.53986
361 94.88666
362 95.29799
363 95.62395
364 96.02876
365 96.37635
366 96.73947
367 97.11601
368 97.49315
369 97.86384
370 98.21651
371 98.6015
372 98.9558
373 99.32242
374 99.69931
375 100.06515
376 100.4321
377 100.7695
378 101.16439
379 101.50733
380 101.88319
381 102.26143
382 102.62986
383 103.0191
384 103.39614
385 103.74803
386 104.07854
387 104.48926
388 104.85846
389 105.18971
390 105.57883
391 105.93445
392 106.31636
393 106.66847
394 107.0377
395 107.45223
396 107.78669
397 108.15341
398 108.50359
399 108.89898
400 109.25877
401 109.6257
402 110.00574
403 110.33136
404 110.70076
405 111.08367
406 111.47131
407 111.80063
408 112.18152
409 112.60016
410 112.90714
411 113.29371
412 113.6652
413 114.03049
414 114.4097
415 114.7575
416 115.12894
417 115.47568
418 115.82707
419 116.23653
420 116.56377
421 116.94788
422 117.31909
423 117.69422
424 118.01311
425 118.39582
426 118.73793
427 119.11572
428 119.4854
429 119.85541
430 120.1937
431 120.56726
432 120.92112
433 121.24601
434 121.64085
435 122.01297
436 122.3769
437 122.73821
438 123.07554
439 123.46651
440 123.81767
441 124.20264
442 124.54846
443 124.90781
444 125.26329
445 125.62878
446 126.00296
447 126.37152
448 126.7131
449 127.08355
450 127.46044
451 127.80919
452 128.14489
453 128.49252
454 128.86867
455 129.25166
456 129.59741
457 129.94568
458 130.28624
459 130.66098
460 131.02991
461 131.38029
462 131.72694
463 132.11462
464 132.44309
465 132.83327
466 133.17344
467 133.51698
468 133.8837
469 134.22139
470 134.59127
471 134.93973
472 135.32127
473 135.65211
474 136.02097
475 136.35423
476 136.71483
477 137.06071
478 137.43918
479 137.78564
480 138.11604
481 138.47576
482 138.83762
483 139.19765
484 139.53505
485 139.92134
486 140.25017
487 140.60218
488 140.96454
489 141.32864
490 141.62091
491 141.97854
492 142.35262
493 142.6989
494 143.05682
495 143.42337
496 143.75626
497 144.09465
498 144.45231
499 144.80242
500 145.16563
501 145.53975
502 145.84266
503 146.18176
504 146.56291
505 146.91727
506 147.2417
507 147.61564
508 147.95694
509 148.2677
510 148.63736
511 148.98394
512 149.34693
513 149.66873
514 150.02218
515 150.36879
516 150.70072
517 151.02821
518 151.43727
519 151.73175
520 152.03932
521 152.40762
522 152.74697
523 153.09363
524 153.43971
525 153.764
526 154.13055
527 154.47458
528 154.79249
529 155.16055
530 155.51085
531 155.81633
532 156.15697
533 156.50643
534 156.86697
535 157.19787
536 157.54612
537 157.85834
538 158.2202
539 158.52279
540 158.88539
541 159.24095
542 159.56804
543 159.88533
544 160.21675
545 160.56119
546 160.90903
547 161.22245
548 161.60198
549 161.90584
550 162.25833
551 162.5985
552 162.92752
553 163.25346
554 163.59696
555 163.91688
556 164.25648
557 164.57274
558 164.92063
559 165.23828
560 165.5478
561 165.90949
562 166.22074
563 166.51884
564 166.91476
565 167.21953
566 167.53172
567 167.89738
568 168.20011
569 168.54925
570 168.86577
571 169.178
572 169.52468
573 169.85109
574 170.1773
575 170.53229
576 170.79028
577 171.15668
578 171.46122
579 171.80799
580 172.11266
581 172.44262
582 172.79354
583 173.09422
584 173.3987
585 173.73796
586 174.09953
587 174.39356
588 174.72627
589 175.04466
590 175.36383
591 175.68159
592 176.00898
593 176.31257
594 176.64832
595 176.95874
596 177.29182
597 177.56505
598 177.93805
599 178.2316
600 178.52124
601 178.87061
602 179.20799
603 179.48469
604 179.84521
605 180.14713
606 180.44905
607 180.76636
608 181.09971
609 181.38463
610 181.76508
611 182.02625
612 182.33076
613 182.66241
614 182.95933
615 183.27327
616 183.59672
617 183.92102
618 184.2231
619 184.54794
620 184.8736
621 185.15971
622 185.47537
623 185.7885
624 186.10104
625 186.40197
626 186.74769
627 187.02964
628 187.33193
629 187.64706
630 187.93257
631 188.26751
632 188.53734
633 188.86462
634 189.1399
635 189.48616
636 189.79404
637 190.09232
638 190.40664
639 190.71293
640 191.00792
641 191.29435
642 191.60093
643 191.92509
644 192.2164
645 192.55483
646 192.8258
647 193.13134
648 193.39966
649 193.7167
650 194.0424
651 194.3365
652 194.62254
653 194.94435
654 195.19412
655 195.51082
656 195.84357
657 196.11363
658 196.41788
659 196.73809
660 197.03563
661 197.32006
662 197.63068
663 197.91103
664 198.21656
665 198.47047
666 198.78324
667 199.0704
668 199.3656
669 199.66506
670 199.97815
671 200.2724
672 200.53845
673 200.82604
674 201.13104
675 201.39445
676 201.72672
677 202.02048
678 202.29088
679 202.59362
680 202.88326
681 203.14419
682 203.45456
683 203.74823
684 204.03446
685 204.31774
686 204.6106
687 204.87802
688 205.15443
689 205.46773
690 205.7568
691 206.07829
692 206.3312
693 206.61929
694 206.90032
695 207.18605
696 207.42385
697 207.71911
698 208.01793
699 208.30888
700 208.60206
701 208.86661
702 209.18256
703 209.43851
704 209.70712
705 209.98855
706 210.31919
707 210.55534
708 210.83975
709 211.11973
710 211.40331
711 211.66007
712 211.93942
713 212.2222
714 212.49081
715 212.78716
716 213.03195
717 213.3288
718 213.65549
719 213.87237
720 214.17744
721 214.45037
722 214.7105
723 215.00134
724 215.2552
725 215.51537
726 215.82499
727 216.07518
728 216.34689
729 216.58217
730 216.89378
731 217.1764
732 217.44176
733 217.69629
734 217.94681
735 218.24068
736 218.51675
737 218.77213
738 219.05559
739 219.30593
740 219.56739
741 219.85393
742 220.11635
743 220.39343
744 220.64395
745 220.90694
746 221.1795
747 221.45101
748 221.69045
749 221.9922
750 222.25441
751 222.5168
752 222.74786
753 223.04353
754 223.25499
755 223.54863
756 223.82379
757 224.06294
758 224.31236
759 224.60526
760 224.82841
761 225.1377
762 225.36327
763 225.60431
764 225.88547
765 226.14425
766 226.3918
767 226.64224
768 226.91715
769 227.15066
770 227.43443
771 227.73025
772 227.94234
773 228.19765
774 228.44256
775 228.75055
776 228.96027
777 229.24267
778 229.4947
779 229.74162
780 229.98372
781 230.24918
782 230.48936
783 230.7452
784 230.96271
785 231.24019
786 231.49182
787 231.73789
788 231.97508
789 232.25389
790 232.4768
791 232.73838
792 232.99342
793 233.218
794 233.50503
795 233.71247
796 233.96224
797 234.24206
798 234.47926
799 234.71863
800 234.94882
801 235.1951
802 235.45089
803 235.68769
804 235.92893
805 236.20011
806 236.43592
807 236.70243
808 236.92284
809 237.16487
810 237.40665
811 237.62638
812 237.8794
813 238.09146
814 238.36405
815 238.5913
816 238.84492
817 239.06493
818 239.32771
819 239.55061
820 239.82958
821 240.02868
822 240.24339
823 240.4883
824 240.72606
825 240.98544
826 241.19052
827 241.44834
828 241.68182
829 241.94075
830 242.14644
831 242.38157
832 242.6218
833 242.88119
834 243.08215
835 243.321
836 243.54479
837 243.73879
838 244.00312
839 244.24446
840 244.49625
841 244.69235
842 244.94308
843 245.16471
844 245.4143
845 245.61782
846 245.86504
847 246.09426
848 246.31316
849 246.53168
850 246.76944
851 246.96727
852 247.20723
853 247.4338
854 247.66239
855 247.90295
856 248.10344
857 248.37537
858 248.59338
859 248.81743
860 249.01171
861 249.26254
862 249.45846
863 249.70406
864 249.90434
865 250.16373
866 250.34844
867 250.58361
868 250.78669
869 251.03517
870 251.2635
871 251.45591
872 251.65087
873 251.88708
874 252.10092
875 252.34004
876 252.54521
877 252.77204
878 252.99023
879 253.20692
880 253.44377
881 253.65623
882 253.87402
883 254.10168
884 254.28353
885 254.51989
886 254.70359
887 254.94836
888 255.15158
889 255.36334
890 255.57503
891 255.78636
892 255.98602
893 256.17308
894 256.42794
895 256.64345
896 256.85016
897 257.05381
898 257.2438
899 257.47135
900 257.68121
901 257.89311
902 258.12292
903 258.33227
904 258.53503
905 258.73638
906 258.97437
907 259.15683
908 259.35759
909 259.5937
910 259.7641
911 259.94891
912 260.20347
913 260.41215
914 260.60668
915 260.80789
916 260.99868
917 261.21735
918 261.41483
919 261.6387
920 261.8327
921 261.99306
922 262.24438
923 262.42561
924 262.63145
925 262.81536
926 263.01419
927 263.24
928 263.43996
929 263.6619
930 263.85757
931 264.05154
932 264.24791
933 264.40714
934 264.63006
935 264.7963
936 265.03519
937 265.23726
938 265.42537
939 265.61832
940 265.81084
941 266.0393
942 266.19979
943 266.36552
944 266.58355
945 266.81486
946 266.9851
947 267.17722
948 267.36573
949 267.56002
950 267.75122
951 267.96043
952 268.17415
953 268.33604
954 268.52844
955 268.71439
956 268.91056
957 269.07025
958 269.28294
959 269.49854
960 269.66783
961 269.87151
962 270.02968
963 270.27383
964 270.43597
965 270.65456
966 270.81764
967 271.00856
968 271.17595
969 271.35836
970 271.5437
971 271.74925
972 271.92799
973 272.09287
974 272.32402
975 272.515
976 272.70194
977 272.87363
978 273.02232
979 273.18437
980 273.38456
981 273.60068
982 273.74085
983 273.97947
984 274.13015
985 274.32472
986 274.51163
987 274.68776
988 274.85989
989 275.05394
990 275.21809
991 275.40923
992 275.5749
993 275.74579
994 275.92871
995 276.15805
996 276.30135
997 276.51321
998 276.70372
999 276.85258
1000 276.98945
1001 277.18597
1002 277.3512
1003 277.55666
1004 277.74276
1005 277.93703
1006 278.08906
1007 278.26892
1008 278.42987
1009 278.5909
1010 278.73465
1011 278.916
1012 279.14415
1013 279.27011
1014 279.49922
1015 279.64448
1016 279.81481
1017 279.98943
1018 280.187
1019 280.3041
1020 280.47
1021 280.68152
1022 280.8099
1023 281.01584
1024 281.1919
1025 281.3569
1026 281.53111
1027 281.68829
1028 281.8784
1029 282.03788
1030 282.17168
1031 282.363
1032 282.56729
1033 282.74188
1034 282.83173
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1471 332.65919
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1500 334.67298
1501 334.74708
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1600 340.8113
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1800 349.76005
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1895 352.84091
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1898 352.91637
1899 352.95025
1900 352.98469
1901 353.02876
1902 353.02028
1903 353.06277
1904 353.06275
1905 353.1236
1906 353.16869
1907 353.17694
1908 353.21763
1909 353.24605
1910 353.26468
1911 353.29373
1912 353.31912
1913 353.33967
1914 353.36816
1915 353.38274
1916 353.42639
1917 353.47178
1918 353.48911
1919 353.51052
1920 353.53232
1921 353.54986
1922 353.58694
1923 353.63283
1924 353.64501
1925 353.69372
1926 353.68501
1927 353.7321
1928 353.75569
1929 353.79852
1930 353.80241
1931 353.83017
1932 353.86111
1933 353.8951
1934 353.92954
1935 353.93237
1936 353.9643
1937 353.98847
1938 354.01908
1939 354.05212
1940 354.08698
1941 354.08852
1942 354.1196
1943 354.15957
1944 354.1842
1945 354.21979
1946 354.24619
1947 354.26842
1948 354.26786
1949 354.30651
1950 354.34991
1951 354.36752
1952 354.38854
1953 354.40991
1954 354.43289
1955 354.46957
1956 354.49878
1957 354.5338
1958 354.53906
1959 354.54508
1960 354.57411
1961 354.62259
1962 354.64489
1963 354.66352
1964 354.6865
1965 354.71189
1966 354.75815
1967 354.76204
1968 354.80241
1969 354.80563
1970 354.83559
1971 354.85713
1972 354.89444
1973 354.93097
1974 354.9319
1975 354.95762
1976 354.9752
1977 355.01483
1978 355.04289
1979 355.06775
1980 355.08499
1981 355.09343
1982 355.12953
1983 355.17541
1984 355.1871
1985 355.20079
1986 355.235
1987 355.23283
1988 355.28591
1989 355.30556
1990 355.34061
1991 355.34676
1992 355.35825
1993 355.40105
1994 355.43458
1995 355.4359
1996 355.4694
1997 355.49379
1998 355.51669
1999 355.529
2000 355.58405
2001 355.58148
2002 355.61301
2003 355.61467
2004 355.6636
2005 355.67483
2006 355.69576
2007 355.70632
2008 355.75542
2009 355.76777
2010 355.77633
2011 355.81655
2012 355.8312
2013 355.84102
2014 355.86767
2015 355.90472
2016 355.92589
2017 355.93985
2018 355.96154
2019 355.97352
2020 356.01295
2021 356.03827
2022 356.05318
2023 356.07553
2024 356.08391
2025 356.11338
2026 356.15299
2027 356.16716
2028 356.19113
2029 356.20483
2030 356.21942
2031 356.25598
2032 356.29022
2033 356.28424
2034 356.31377
2035 356.32014
2036 356.35179
2037 356.38465
2038 356.41186
2039 356.42356
2040 356.44847
2041 356.47144
2042 356.48884
2043 356.51738
2044 356.52381
2045 356.54682
2046 356.57101
2047 356.60499
2048 356.61408
2049 356.62772
2050 356.65839
2051 356.66249
2052 356.696
2053 356.72687
2054 356.72733
2055 356.75516
2056 356.77478
2057 356.79932
2058 356.824
2059 356.83313
2060 356.84128
2061 356.87255
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