Let
m*n=w (i)
m is a 3-digit number
so is n
w is a 6-digit number
In equation (i) only 4 distinct digits are used.
Find the possible equations.
Finding one such example in the secondary challenge led to the thought there may be more multiplications that require only 3 different digits. Indeed there are 127, from among those that met the 4-digit version. (There was no check in the original program to make sure that exactly 4 were used.)
There are no cases with only two different digits and still have a 6-digit result.
101 991 100091
110 910 100100
110 919 101090
110 991 109010
111 901 100011
111 910 101010
111 991 110001
119 999 118881
121 919 111199
121 991 119911
168 666 111888
188 861 161868
189 999 188811
191 989 188899
211 911 192221
221 777 171717
285 885 252225
288 848 244224
313 355 111115
333 335 111555
335 333 111555
355 313 111115
393 933 366669
445 545 242525
445 999 444555
455 555 252525
455 999 454545
488 888 433344
500 500 250000
500 505 252500
505 500 252500
505 505 255025
545 445 242525
545 999 544455
555 455 252525
555 995 552225
555 999 554445
600 600 360000
600 606 363600
606 600 363600
646 688 444448
664 666 442224
666 168 111888
666 664 442224
666 668 444888
666 996 663336
668 666 444888
669 995 665655
686 858 588588
688 646 444448
715 777 555555
750 770 577500
755 765 577575
765 755 577575
766 886 678676
770 750 577500
777 221 171717
777 715 555555
777 975 757575
800 860 688000
819 999 818181
847 884 748748
848 288 244224
858 686 588588
860 800 688000
861 188 161868
876 888 777888
877 887 777899
877 888 778776
878 887 778786
884 847 748748
885 285 252225
886 766 678676
886 888 786768
887 877 777899
887 878 778786
888 488 433344
888 876 777888
888 877 778776
888 886 786768
889 999 888111
891 989 881199
898 991 889918
899 911 818989
899 981 881919
899 989 889111
901 111 100011
901 999 900099
910 110 100100
910 111 101010
910 990 900900
910 999 909090
911 211 192221
911 899 818989
919 110 101090
919 121 111199
926 996 922296
933 393 366669
962 966 929292
966 962 929292
975 777 757575
981 899 881919
989 191 188899
989 891 881199
989 899 889111
990 910 900900
991 101 100091
991 110 109010
991 111 110001
991 121 119911
991 898 889918
991 999 990009
995 555 552225
995 669 665655
996 666 663336
996 926 922296
999 119 118881
999 189 188811
999 445 444555
999 455 454545
999 545 544455
999 555 554445
999 819 818181
999 889 888111
999 901 900099
999 910 909090
999 991 990009
|
|
Posted by Charlie
on 2017-12-03 12:03:10 |
just 3 different digits
