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Three conditions define a triplet (Posted on 2015-01-14) Difficulty: 3 of 5
Let N denote an integer number such that:

I. N is a 3-digit number abc.
ii. a,b,c are distinct non-zero decimal digits.
iii. The product a*b*c divides N.

List all possible values for (a,b,c) complying with the above conditions.

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution Comment 2 of 2 |
 For n = 100 To 999
   s$ = LTrim(Str(n))
   prod = 1: good = 1
   For i = 1 To Len(s$)
     prod = prod * Val(Mid(s$, i, 1))
     If InStr(s$, Mid(s$, i, 1)) <> i Or prod = 0 Then
       good = 0
       Exit For
     End If
    Next
    If good Then
     ct = ct + 1
     If n Mod prod = 0 Then
      Text1.Text = Text1.Text & n & Str(prod) & crlf
      goodct = goodct + 1
     End If
    End If
 Next

N   product of digits
128 16
132 6
135 15
175 35
216 12
312 6
315 15
384 96
432 24
612 12
624 48
672 84
735 105
816 48

  Posted by Charlie on 2015-01-14 22:24:18
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