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Just 4 different digits (Posted on 2017-12-03) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
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just 3 different digits | Comment 6 of 10 |
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
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