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Sixes and Sevens (Posted on 2014-08-02) Difficulty: 3 of 5
Find the smallest positive integer multiple of 84 whose base ten representation uses only the two digits 6 and 7.

No Solution Yet Submitted by K Sengupta    
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Solution computer solution | Comment 1 of 4
DefDbl A-Z
Dim crlf$

Private Sub Form_Load()
 ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents
 
 m = 84
 For i = 2 To 10000000
   m = m + 84
   ms$ = LTrim$(Str$(m))
   good = 1
   For j = 1 To Len(ms$)
     If InStr("67", Mid(ms$, j, 1)) = 0 Then good = 0
   Next
   If good Then
    Text1.Text = Text1.Text & i & Str(m) & crlf
    DoEvents
   End If
 Next
 
 Text1.Text = Text1.Text & crlf & "done"
End Sub

finds

mult.   product 
914     76776
9139   767676
91389   7676676
793664 66667776
913889 76766676
925914 77776776
7936639 666677676
7948414 667666776
8068664 677767776
9138889 767666676
9246164 776677776
9259139 777767676

There seems to be a pattern in 9138...89 as the multiplier for 84 producing 76766...676, plus other patterns possibly forming.

The lowest, as answer to the puzzle, is 914 * 84 = 76776.


  Posted by Charlie on 2014-08-02 14:26:11
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