If rule 7 is taken strictly, that is without regard to the order of the multiplicands, in neither order do the partial products contain the digit u, there is only one solution:
874
874
-------
3496
6118
6992
-------
763876
With rule 7 taken more loosely there are other solutions, still using rule 7:
n1 n2 product
328 626 205328
329 625 205625
735 438 321930
736 437 321632
873 875 763875
874 874 763876
For example:
328 but 626
x 626 x 328
------ ------
1968 5008 reversing the multiplicands
656 1252 puts u into partial products
1968 1878
------ ------
205328 205328
Eliminating rule 7 altogether:
n1 n2 product
212 518 109816
212 718 152216
212 818 173416
212 918 194616
214 715 153010
214 815 174410
214 915 195810
215 614 132010
215 714 153510
215 814 175010
215 914 196510
218 612 133416
218 712 155216
218 812 177016
218 912 198816
312 418 130416
312 618 192816
314 415 130310
315 414 130410
315 614 193410
318 512 162816
318 612 194616
320 626 200320
320 721 230720
320 826 264320
320 921 294720
320 926 296320
321 625 200625
321 720 231120
321 825 264825
321 920 295320
321 925 296925
323 723 233529
323 727 234821
323 823 265829
323 827 267121
323 923 298129
323 927 299421
324 826 267624
325 621 201825
325 625 203125
325 629 204425
325 721 234325
325 725 235625
325 729 236925
325 821 266825
325 825 268125
325 829 269425
325 921 299325
326 624 203424
326 628 204728
326 720 234720
326 724 236024
326 728 237328
326 820 267320
326 824 268624
326 828 269928
326 920 299920
327 623 203721
327 627 205029
327 723 236421
327 727 237729
327 823 269121
327 827 270429
328 626 205328
328 726 238128
328 826 270928
329 625 205625
329 725 238525
329 825 271425
412 418 172216
420 521 218820
420 621 260820
421 520 218920
421 620 261020
421 625 263125
423 623 263529
424 626 265424
425 621 263925
425 625 265625
425 629 267325
426 620 264120
426 624 265824
426 628 267528
427 623 266021
427 627 267729
428 626 267928
429 625 268125
431 730 314630
431 830 357730
435 738 321030
435 838 364530
436 837 364932
437 736 321632
438 735 321930
438 835 365730
520 521 270920
520 526 273520
521 525 273525
523 523 273529
523 527 275621
524 526 275624
525 525 275625
525 529 277725
526 528 277728
527 527 277729
530 731 387430
531 730 387630
535 738 394830
536 637 341432
536 737 395032
537 636 341532
537 736 395232
538 635 341630
538 735 395430
540 741 400140
540 746 402840
540 846 456840
541 740 400340
541 745 403045
541 845 457145
543 843 457749
545 741 403845
545 841 458345
546 840 458640
630 631 397530
640 641 410240
641 745 477545
643 743 477749
645 741 477945
646 740 478040
659 850 560150
750 751 563250
750 753 564750
750 757 567750
750 759 569250
751 752 564752
751 754 566254
751 756 567756
751 758 569258
752 753 566256
760 861 654360
761 860 654460
761 865 658265
762 864 658368
763 863 658469
764 862 658568
872 876 763872
873 875 763875
874 874 763876
As partial products are not a question here, both orders of multiplicand word, so only n1 <= n2 are shown:
Text1.Text = ""
For n1 = 100 To 999
n1s$ = LTrim(Str(n1))
u$ = Mid(n1s$, 2, 1)
For a = 1 To 9
For c = 0 To 9
n2 = 100 * a + 10 * Val(u$) + c
prod = n1 * n2
prods$ = LTrim(Str(prod))
If Len(prods$) = 6 Then
If Left(prods$, 1) = u$ And Mid(prods$, 5, 1) = u$ Then
n2s$ = LTrim(Str(n2))
If Left(n1s$, 1) <> u$ And Right(n1s$, 1) <> u$ And Left(n2s$, 1) <> u$ And Right(n2s$, 1) <> u$ Then
If InStr(Mid(prods$, 2, 3) + Right(prods$, 1), u$) = 0 Then
pp1s$ = LTrim(Str(n1 * c))
pp2s$ = LTrim(Str(n1 * Val(u$)))
pp3s$ = LTrim(Str(n1 * a))
a1 = n1 \ 100: c1 = n1 Mod 10
tst$ = LTrim(Str(a1 * n2)) + LTrim(Str(Val(u$) * n2)) + LTrim(Str(c1 * n2))
' If InStr(tst$, u$) = 0 Then
' If InStr(pp1s$ + pp2s$ + pp3s$, u$) = 0 Then
If n2 >= n1 Then
Text1.Text = Text1.Text & Str(n1) & Str(n2) & Str(prod) & Chr(13) & Chr(10)
End If
' End If
' End If
End If
End If
End If
End If
Next
Next
Next
Commented lines (with leading apostrophe) were used for the more strict listings, but without the n2 >= n1 stricture.
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Posted by Charlie
on 2014-04-30 16:33:40 |
computer solution
