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 Sixes and Sevens (Posted on 2014-08-02)
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 No Rating

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 computer solution | Comment 1 of 4
DefDbl A-Z
Dim crlf\$

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     767769139   	76767691389  	7676676793664 	66667776913889 	76766676925914 	777767767936639 6666776767948414 6676667768068664 6777677769138889 7676666769246164 7766777769259139 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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