AlgoritmalarMatematik

Sihirli Sayılar – Tip 2

Sayılarla ilgili sonsuz sayıda özellik vardır. Buradaki amaçlarımız; hem bunu hem de nasıl bulduğumuzu göstererek özellikle matematiksel programlama konusunda katkı sağlamaktır.

Bu defa; 100-1000 arasında ve şu özelliğe sahip sayılar buldum. (Yazdığım bilgisayar kodu en alttadır.)

x çarpma operatörü, a, b, c, d, e, f rakamlar ve (y1) (y2) (y3) bir sayı olmak üzere:
abc x def = (y1) (y2) (y3) iken cba x fed = (y3) (y2) (y1) olmaktadır.

 102 x 103 = 10506 ; 201 x 301 = 60501
 102 x 104 = 10608 ; 201 x 401 = 80601
 102 x 112 = 11424 ; 201 x 211 = 42411
 102 x 113 = 11526 ; 201 x 311 = 62511
 102 x 114 = 11628 ; 201 x 411 = 82611
 102 x 122 = 12444 ; 201 x 221 = 44421
 102 x 123 = 12546 ; 201 x 321 = 64521
 102 x 124 = 12648 ; 201 x 421 = 84621
 102 x 132 = 13464 ; 201 x 231 = 46431
 102 x 133 = 13566 ; 201 x 331 = 66531
 102 x 134 = 13668 ; 201 x 431 = 86631
 102 x 142 = 14484 ; 201 x 241 = 48441
 102 x 143 = 14586 ; 201 x 341 = 68541
 102 x 144 = 14688 ; 201 x 441 = 88641
 102 x 201 = 20502 ; 201 x 102 = 20502
 102 x 203 = 20706 ; 201 x 302 = 60702
 102 x 204 = 20808 ; 201 x 402 = 80802
 102 x 211 = 21522 ; 201 x 112 = 22512
 102 x 213 = 21726 ; 201 x 312 = 62712
 102 x 214 = 21828 ; 201 x 412 = 82812
 102 x 221 = 22542 ; 201 x 122 = 24522
 102 x 223 = 22746 ; 201 x 322 = 64722
 102 x 224 = 22848 ; 201 x 422 = 84822
 102 x 231 = 23562 ; 201 x 132 = 26532
 102 x 233 = 23766 ; 201 x 332 = 66732
 102 x 234 = 23868 ; 201 x 432 = 86832
 102 x 241 = 24582 ; 201 x 142 = 28542
 102 x 243 = 24786 ; 201 x 342 = 68742
 102 x 244 = 24888 ; 201 x 442 = 88842
 102 x 301 = 30702 ; 201 x 103 = 20703
 102 x 302 = 30804 ; 201 x 203 = 40803
 102 x 311 = 31722 ; 201 x 113 = 22713
 102 x 312 = 31824 ; 201 x 213 = 42813
 102 x 321 = 32742 ; 201 x 123 = 24723
 102 x 322 = 32844 ; 201 x 223 = 44823
 102 x 331 = 33762 ; 201 x 133 = 26733
 102 x 332 = 33864 ; 201 x 233 = 46833
 102 x 341 = 34782 ; 201 x 143 = 28743
 102 x 342 = 34884 ; 201 x 243 = 48843
 102 x 401 = 40902 ; 201 x 104 = 20904
 102 x 411 = 41922 ; 201 x 114 = 22914
 102 x 421 = 42942 ; 201 x 124 = 24924
 102 x 431 = 43962 ; 201 x 134 = 26934
 102 x 441 = 44982 ; 201 x 144 = 28944
 103 x 102 = 10506 ; 301 x 201 = 60501
 103 x 112 = 11536 ; 301 x 211 = 63511
 103 x 113 = 11639 ; 301 x 311 = 93611
 103 x 122 = 12566 ; 301 x 221 = 66521
 103 x 123 = 12669 ; 301 x 321 = 96621
 103 x 132 = 13596 ; 301 x 231 = 69531
 103 x 133 = 13699 ; 301 x 331 = 99631
 103 x 201 = 20703 ; 301 x 102 = 30702
 103 x 203 = 20909 ; 301 x 302 = 90902
 103 x 211 = 21733 ; 301 x 112 = 33712
 103 x 213 = 21939 ; 301 x 312 = 93912
 103 x 221 = 22763 ; 301 x 122 = 36722
 103 x 223 = 22969 ; 301 x 322 = 96922
 103 x 231 = 23793 ; 301 x 132 = 39732
 103 x 233 = 23999 ; 301 x 332 = 99932
 104 x 102 = 10608 ; 401 x 201 = 80601
 104 x 112 = 11648 ; 401 x 211 = 84611
 104 x 122 = 12688 ; 401 x 221 = 88621
 104 x 201 = 20904 ; 401 x 102 = 40902
 104 x 211 = 21944 ; 401 x 112 = 44912
 104 x 221 = 22984 ; 401 x 122 = 48922
 112 x 102 = 11424 ; 211 x 201 = 42411
 112 x 103 = 11536 ; 211 x 301 = 63511
 112 x 104 = 11648 ; 211 x 401 = 84611
 112 x 113 = 12656 ; 211 x 311 = 65621
 112 x 114 = 12768 ; 211 x 411 = 86721
 112 x 122 = 13664 ; 211 x 221 = 46631
 112 x 123 = 13776 ; 211 x 321 = 67731
 112 x 124 = 13888 ; 211 x 421 = 88831
 112 x 132 = 14784 ; 211 x 231 = 48741
 112 x 133 = 14896 ; 211 x 331 = 69841
 112 x 201 = 22512 ; 211 x 102 = 21522
 112 x 203 = 22736 ; 211 x 302 = 63722
 112 x 204 = 22848 ; 211 x 402 = 84822
 112 x 211 = 23632 ; 211 x 112 = 23632
 112 x 213 = 23856 ; 211 x 312 = 65832
 112 x 214 = 23968 ; 211 x 412 = 86932
 112 x 221 = 24752 ; 211 x 122 = 25742
 112 x 223 = 24976 ; 211 x 322 = 67942
 112 x 231 = 25872 ; 211 x 132 = 27852
 112 x 241 = 26992 ; 211 x 142 = 29962
 112 x 301 = 33712 ; 211 x 103 = 21733
 112 x 302 = 33824 ; 211 x 203 = 42833
 112 x 311 = 34832 ; 211 x 113 = 23843
 112 x 312 = 34944 ; 211 x 213 = 44943
 112 x 321 = 35952 ; 211 x 123 = 25953
 112 x 401 = 44912 ; 211 x 104 = 21944
 113 x 102 = 11526 ; 311 x 201 = 62511
 113 x 103 = 11639 ; 311 x 301 = 93611
 113 x 112 = 12656 ; 311 x 211 = 65621
 113 x 122 = 13786 ; 311 x 221 = 68731
 113 x 123 = 13899 ; 311 x 321 = 99831
 113 x 201 = 22713 ; 311 x 102 = 31722
 113 x 203 = 22939 ; 311 x 302 = 93922
 113 x 211 = 23843 ; 311 x 112 = 34832
 113 x 221 = 24973 ; 311 x 122 = 37942
 114 x 102 = 11628 ; 411 x 201 = 82611
 114 x 112 = 12768 ; 411 x 211 = 86721
 114 x 201 = 22914 ; 411 x 102 = 41922
 122 x 102 = 12444 ; 221 x 201 = 44421
 122 x 103 = 12566 ; 221 x 301 = 66521
 122 x 104 = 12688 ; 221 x 401 = 88621
 122 x 112 = 13664 ; 221 x 211 = 46631
 122 x 113 = 13786 ; 221 x 311 = 68731
 122 x 201 = 24522 ; 221 x 102 = 22542
 122 x 203 = 24766 ; 221 x 302 = 66742
 122 x 204 = 24888 ; 221 x 402 = 88842
 122 x 211 = 25742 ; 221 x 112 = 24752
 122 x 213 = 25986 ; 221 x 312 = 68952
 122 x 221 = 26962 ; 221 x 122 = 26962
 122 x 301 = 36722 ; 221 x 103 = 22763
 122 x 302 = 36844 ; 221 x 203 = 44863
 122 x 311 = 37942 ; 221 x 113 = 24973
 122 x 401 = 48922 ; 221 x 104 = 22984
 123 x 102 = 12546 ; 321 x 201 = 64521
 123 x 103 = 12669 ; 321 x 301 = 96621
 123 x 112 = 13776 ; 321 x 211 = 67731
 123 x 113 = 13899 ; 321 x 311 = 99831
 123 x 201 = 24723 ; 321 x 102 = 32742
 123 x 203 = 24969 ; 321 x 302 = 96942
 123 x 211 = 25953 ; 321 x 112 = 35952
 124 x 102 = 12648 ; 421 x 201 = 84621
 124 x 112 = 13888 ; 421 x 211 = 88831
 124 x 201 = 24924 ; 421 x 102 = 42942
 132 x 102 = 13464 ; 231 x 201 = 46431
 132 x 103 = 13596 ; 231 x 301 = 69531
 132 x 112 = 14784 ; 231 x 211 = 48741
 132 x 201 = 26532 ; 231 x 102 = 23562
 132 x 203 = 26796 ; 231 x 302 = 69762
 132 x 211 = 27852 ; 231 x 112 = 25872
 132 x 301 = 39732 ; 231 x 103 = 23793
 132 x 302 = 39864 ; 231 x 203 = 46893
 133 x 102 = 13566 ; 331 x 201 = 66531
 133 x 103 = 13699 ; 331 x 301 = 99631
 133 x 112 = 14896 ; 331 x 211 = 69841
 133 x 201 = 26733 ; 331 x 102 = 33762
 133 x 203 = 26999 ; 331 x 302 = 99962
 134 x 102 = 13668 ; 431 x 201 = 86631
 134 x 201 = 26934 ; 431 x 102 = 43962
 142 x 102 = 14484 ; 241 x 201 = 48441
 142 x 201 = 28542 ; 241 x 102 = 24582
 142 x 211 = 29962 ; 241 x 112 = 26992
 143 x 102 = 14586 ; 341 x 201 = 68541
 143 x 201 = 28743 ; 341 x 102 = 34782
 144 x 102 = 14688 ; 441 x 201 = 88641
 144 x 201 = 28944 ; 441 x 102 = 44982
 201 x 102 = 20502 ; 102 x 201 = 20502
 201 x 103 = 20703 ; 102 x 301 = 30702
 201 x 104 = 20904 ; 102 x 401 = 40902
 201 x 112 = 22512 ; 102 x 211 = 21522
 201 x 113 = 22713 ; 102 x 311 = 31722
 201 x 114 = 22914 ; 102 x 411 = 41922
 201 x 122 = 24522 ; 102 x 221 = 22542
 201 x 123 = 24723 ; 102 x 321 = 32742
 201 x 124 = 24924 ; 102 x 421 = 42942
 201 x 132 = 26532 ; 102 x 231 = 23562
 201 x 133 = 26733 ; 102 x 331 = 33762
 201 x 134 = 26934 ; 102 x 431 = 43962
 201 x 142 = 28542 ; 102 x 241 = 24582
 201 x 143 = 28743 ; 102 x 341 = 34782
 201 x 144 = 28944 ; 102 x 441 = 44982
 201 x 203 = 40803 ; 102 x 302 = 30804
 201 x 211 = 42411 ; 102 x 112 = 11424
 201 x 213 = 42813 ; 102 x 312 = 31824
 201 x 221 = 44421 ; 102 x 122 = 12444
 201 x 223 = 44823 ; 102 x 322 = 32844
 201 x 231 = 46431 ; 102 x 132 = 13464
 201 x 233 = 46833 ; 102 x 332 = 33864
 201 x 241 = 48441 ; 102 x 142 = 14484
 201 x 243 = 48843 ; 102 x 342 = 34884
 201 x 301 = 60501 ; 102 x 103 = 10506
 201 x 302 = 60702 ; 102 x 203 = 20706
 201 x 311 = 62511 ; 102 x 113 = 11526
 201 x 312 = 62712 ; 102 x 213 = 21726
 201 x 321 = 64521 ; 102 x 123 = 12546
 201 x 322 = 64722 ; 102 x 223 = 22746
 201 x 331 = 66531 ; 102 x 133 = 13566
 201 x 332 = 66732 ; 102 x 233 = 23766
 201 x 341 = 68541 ; 102 x 143 = 14586
 201 x 342 = 68742 ; 102 x 243 = 24786
 201 x 401 = 80601 ; 102 x 104 = 10608
 201 x 402 = 80802 ; 102 x 204 = 20808
 201 x 411 = 82611 ; 102 x 114 = 11628
 201 x 412 = 82812 ; 102 x 214 = 21828
 201 x 421 = 84621 ; 102 x 124 = 12648
 201 x 422 = 84822 ; 102 x 224 = 22848
 201 x 431 = 86631 ; 102 x 134 = 13668
 201 x 432 = 86832 ; 102 x 234 = 23868
 201 x 441 = 88641 ; 102 x 144 = 14688
 201 x 442 = 88842 ; 102 x 244 = 24888
 203 x 102 = 20706 ; 302 x 201 = 60702
 203 x 103 = 20909 ; 302 x 301 = 90902
 203 x 112 = 22736 ; 302 x 211 = 63722
 203 x 113 = 22939 ; 302 x 311 = 93922
 203 x 122 = 24766 ; 302 x 221 = 66742
 203 x 123 = 24969 ; 302 x 321 = 96942
 203 x 132 = 26796 ; 302 x 231 = 69762
 203 x 133 = 26999 ; 302 x 331 = 99962
 203 x 201 = 40803 ; 302 x 102 = 30804
 203 x 211 = 42833 ; 302 x 112 = 33824
 203 x 221 = 44863 ; 302 x 122 = 36844
 203 x 231 = 46893 ; 302 x 132 = 39864
 204 x 102 = 20808 ; 402 x 201 = 80802
 204 x 112 = 22848 ; 402 x 211 = 84822
 204 x 122 = 24888 ; 402 x 221 = 88842
 211 x 102 = 21522 ; 112 x 201 = 22512
 211 x 103 = 21733 ; 112 x 301 = 33712
 211 x 104 = 21944 ; 112 x 401 = 44912
 211 x 112 = 23632 ; 112 x 211 = 23632
 211 x 113 = 23843 ; 112 x 311 = 34832
 211 x 122 = 25742 ; 112 x 221 = 24752
 211 x 123 = 25953 ; 112 x 321 = 35952
 211 x 132 = 27852 ; 112 x 231 = 25872
 211 x 142 = 29962 ; 112 x 241 = 26992
 211 x 201 = 42411 ; 112 x 102 = 11424
 211 x 203 = 42833 ; 112 x 302 = 33824
 211 x 213 = 44943 ; 112 x 312 = 34944
 211 x 221 = 46631 ; 112 x 122 = 13664
 211 x 231 = 48741 ; 112 x 132 = 14784
 211 x 301 = 63511 ; 112 x 103 = 11536
 211 x 302 = 63722 ; 112 x 203 = 22736
 211 x 311 = 65621 ; 112 x 113 = 12656
 211 x 312 = 65832 ; 112 x 213 = 23856
 211 x 321 = 67731 ; 112 x 123 = 13776
 211 x 322 = 67942 ; 112 x 223 = 24976
 211 x 331 = 69841 ; 112 x 133 = 14896
 211 x 401 = 84611 ; 112 x 104 = 11648
 211 x 402 = 84822 ; 112 x 204 = 22848
 211 x 411 = 86721 ; 112 x 114 = 12768
 211 x 412 = 86932 ; 112 x 214 = 23968
 211 x 421 = 88831 ; 112 x 124 = 13888
 213 x 102 = 21726 ; 312 x 201 = 62712
 213 x 103 = 21939 ; 312 x 301 = 93912
 213 x 112 = 23856 ; 312 x 211 = 65832
 213 x 122 = 25986 ; 312 x 221 = 68952
 213 x 201 = 42813 ; 312 x 102 = 31824
 213 x 211 = 44943 ; 312 x 112 = 34944
 214 x 102 = 21828 ; 412 x 201 = 82812
 214 x 112 = 23968 ; 412 x 211 = 86932
 221 x 102 = 22542 ; 122 x 201 = 24522
 221 x 103 = 22763 ; 122 x 301 = 36722
 221 x 104 = 22984 ; 122 x 401 = 48922
 221 x 112 = 24752 ; 122 x 211 = 25742
 221 x 113 = 24973 ; 122 x 311 = 37942
 221 x 122 = 26962 ; 122 x 221 = 26962
 221 x 201 = 44421 ; 122 x 102 = 12444
 221 x 203 = 44863 ; 122 x 302 = 36844
 221 x 211 = 46631 ; 122 x 112 = 13664
 221 x 301 = 66521 ; 122 x 103 = 12566
 221 x 302 = 66742 ; 122 x 203 = 24766
 221 x 311 = 68731 ; 122 x 113 = 13786
 221 x 312 = 68952 ; 122 x 213 = 25986
 221 x 401 = 88621 ; 122 x 104 = 12688
 221 x 402 = 88842 ; 122 x 204 = 24888
 223 x 102 = 22746 ; 322 x 201 = 64722
 223 x 103 = 22969 ; 322 x 301 = 96922
 223 x 112 = 24976 ; 322 x 211 = 67942
 223 x 201 = 44823 ; 322 x 102 = 32844
 224 x 102 = 22848 ; 422 x 201 = 84822
 231 x 102 = 23562 ; 132 x 201 = 26532
 231 x 103 = 23793 ; 132 x 301 = 39732
 231 x 112 = 25872 ; 132 x 211 = 27852
 231 x 201 = 46431 ; 132 x 102 = 13464
 231 x 203 = 46893 ; 132 x 302 = 39864
 231 x 211 = 48741 ; 132 x 112 = 14784
 231 x 301 = 69531 ; 132 x 103 = 13596
 231 x 302 = 69762 ; 132 x 203 = 26796
 233 x 102 = 23766 ; 332 x 201 = 66732
 233 x 103 = 23999 ; 332 x 301 = 99932
 233 x 201 = 46833 ; 332 x 102 = 33864
 234 x 102 = 23868 ; 432 x 201 = 86832
 241 x 102 = 24582 ; 142 x 201 = 28542
 241 x 112 = 26992 ; 142 x 211 = 29962
 241 x 201 = 48441 ; 142 x 102 = 14484
 243 x 102 = 24786 ; 342 x 201 = 68742
 243 x 201 = 48843 ; 342 x 102 = 34884
 244 x 102 = 24888 ; 442 x 201 = 88842
 301 x 102 = 30702 ; 103 x 201 = 20703
 301 x 112 = 33712 ; 103 x 211 = 21733
 301 x 122 = 36722 ; 103 x 221 = 22763
 301 x 132 = 39732 ; 103 x 231 = 23793
 301 x 201 = 60501 ; 103 x 102 = 10506
 301 x 211 = 63511 ; 103 x 112 = 11536
 301 x 221 = 66521 ; 103 x 122 = 12566
 301 x 231 = 69531 ; 103 x 132 = 13596
 301 x 302 = 90902 ; 103 x 203 = 20909
 301 x 311 = 93611 ; 103 x 113 = 11639
 301 x 312 = 93912 ; 103 x 213 = 21939
 301 x 321 = 96621 ; 103 x 123 = 12669
 301 x 322 = 96922 ; 103 x 223 = 22969
 301 x 331 = 99631 ; 103 x 133 = 13699
 301 x 332 = 99932 ; 103 x 233 = 23999
 302 x 102 = 30804 ; 203 x 201 = 40803
 302 x 112 = 33824 ; 203 x 211 = 42833
 302 x 122 = 36844 ; 203 x 221 = 44863
 302 x 132 = 39864 ; 203 x 231 = 46893
 302 x 201 = 60702 ; 203 x 102 = 20706
 302 x 211 = 63722 ; 203 x 112 = 22736
 302 x 221 = 66742 ; 203 x 122 = 24766
 302 x 231 = 69762 ; 203 x 132 = 26796
 302 x 301 = 90902 ; 203 x 103 = 20909
 302 x 311 = 93922 ; 203 x 113 = 22939
 302 x 321 = 96942 ; 203 x 123 = 24969
 302 x 331 = 99962 ; 203 x 133 = 26999
 311 x 102 = 31722 ; 113 x 201 = 22713
 311 x 112 = 34832 ; 113 x 211 = 23843
 311 x 122 = 37942 ; 113 x 221 = 24973
 311 x 201 = 62511 ; 113 x 102 = 11526
 311 x 211 = 65621 ; 113 x 112 = 12656
 311 x 221 = 68731 ; 113 x 122 = 13786
 311 x 301 = 93611 ; 113 x 103 = 11639
 311 x 302 = 93922 ; 113 x 203 = 22939
 311 x 321 = 99831 ; 113 x 123 = 13899
 312 x 102 = 31824 ; 213 x 201 = 42813
 312 x 112 = 34944 ; 213 x 211 = 44943
 312 x 201 = 62712 ; 213 x 102 = 21726
 312 x 211 = 65832 ; 213 x 112 = 23856
 312 x 221 = 68952 ; 213 x 122 = 25986
 312 x 301 = 93912 ; 213 x 103 = 21939
 321 x 102 = 32742 ; 123 x 201 = 24723
 321 x 112 = 35952 ; 123 x 211 = 25953
 321 x 201 = 64521 ; 123 x 102 = 12546
 321 x 211 = 67731 ; 123 x 112 = 13776
 321 x 301 = 96621 ; 123 x 103 = 12669
 321 x 302 = 96942 ; 123 x 203 = 24969
 321 x 311 = 99831 ; 123 x 113 = 13899
 322 x 102 = 32844 ; 223 x 201 = 44823
 322 x 201 = 64722 ; 223 x 102 = 22746
 322 x 211 = 67942 ; 223 x 112 = 24976
 322 x 301 = 96922 ; 223 x 103 = 22969
 331 x 102 = 33762 ; 133 x 201 = 26733
 331 x 201 = 66531 ; 133 x 102 = 13566
 331 x 211 = 69841 ; 133 x 112 = 14896
 331 x 301 = 99631 ; 133 x 103 = 13699
 331 x 302 = 99962 ; 133 x 203 = 26999
 332 x 102 = 33864 ; 233 x 201 = 46833
 332 x 201 = 66732 ; 233 x 102 = 23766
 332 x 301 = 99932 ; 233 x 103 = 23999
 341 x 102 = 34782 ; 143 x 201 = 28743
 341 x 201 = 68541 ; 143 x 102 = 14586
 342 x 102 = 34884 ; 243 x 201 = 48843
 342 x 201 = 68742 ; 243 x 102 = 24786
 401 x 102 = 40902 ; 104 x 201 = 20904
 401 x 112 = 44912 ; 104 x 211 = 21944
 401 x 122 = 48922 ; 104 x 221 = 22984
 401 x 201 = 80601 ; 104 x 102 = 10608
 401 x 211 = 84611 ; 104 x 112 = 11648
 401 x 221 = 88621 ; 104 x 122 = 12688
 402 x 201 = 80802 ; 204 x 102 = 20808
 402 x 211 = 84822 ; 204 x 112 = 22848
 402 x 221 = 88842 ; 204 x 122 = 24888
 411 x 102 = 41922 ; 114 x 201 = 22914
 411 x 201 = 82611 ; 114 x 102 = 11628
 411 x 211 = 86721 ; 114 x 112 = 12768
 412 x 201 = 82812 ; 214 x 102 = 21828
 412 x 211 = 86932 ; 214 x 112 = 23968
 421 x 102 = 42942 ; 124 x 201 = 24924
 421 x 201 = 84621 ; 124 x 102 = 12648
 421 x 211 = 88831 ; 124 x 112 = 13888
 422 x 201 = 84822 ; 224 x 102 = 22848
 431 x 102 = 43962 ; 134 x 201 = 26934
 431 x 201 = 86631 ; 134 x 102 = 13668
 432 x 201 = 86832 ; 234 x 102 = 23868
 441 x 102 = 44982 ; 144 x 201 = 28944
 441 x 201 = 88641 ; 144 x 102 = 14688
 442 x 201 = 88842 ; 244 x 102 = 24888

Tüm sayılar bilgisayar tarafından 2 dakikada bulunmuştur. 
Bu hesaplamayı yapan yazdığım C# kodu:
[snippet id="539"]

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