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 Identical Digit Baffle (Posted on 2014-09-08)
Determine the largest five digit base-14 positive integer such that when multiplied by a single base-14 digit, the result is a six digit base-14 positive integer with all digits identical.

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution | Comment 1 of 2
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

For repdigit = 1 To 13
repdnum = Int(repdigit * (14 ^ 6 - 1) / 13 + 0.5)
For divsr = 1 To 13
q = repdnum / divsr
If Int(q) = q Then
b14\$ = base\$(q, 14)
If Len(b14\$) = 5 Then
Text1.Text = Text1.Text & b14\$ & "(" & (q) & ")" & "   " & base\$(repdnum, 14)
Text1.Text = Text1.Text & "(" & (repdnum) & ")"
Text1.Text = Text1.Text & "    " & base\$(divsr, 14) & crlf
End If
End If
Next
Next

Text1.Text = Text1.Text & crlf & " done"
End Sub

Function base\$(n, b)
v\$ = ""
n2 = n
Do
d = n2 Mod b
n2 = n2 \ b
v\$ = Mid("0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ", d + 1, 1) + v\$
Loop Until n2 = 0
base\$ = v\$
End Function

finds, (lines sorted by a separate step), this list of all such 5-digit base-14 integers:

`base-14  decimal	 productinteger	 equivalent   base-14 decimal  multiplier1964B    (64355)      111111(579195)     930303	 (115839)     111111(579195)     530303	 (115839)     222222(1158390)    A34C98	 (128710)     222222(1158390)    950505	 (193065)     111111(579195)     350505	 (193065)     222222(1158390)    650505	 (193065)     333333(1737585)    950505	 (193065)     444444(2316780)    C60606	 (231678)     222222(1158390)    560606	 (231678)     444444(2316780)    A69B52	 (257420)     444444(2316780)    98539D	 (321775)     555555(2895975)    990909	 (347517)     333333(1737585)    590909	 (347517)     666666(3475170)    AA0A0A	 (386130)     222222(1158390)    3A0A0A	 (386130)     444444(2316780)    6A0A0A	 (386130)     666666(3475170)    9A0A0A	 (386130)     888888(4633560)    CBA257	 (450485)     777777(4054365)    9C0C0C	 (463356)     444444(2316780)    5C0C0C	 (463356)     888888(4633560)    AD58A4	 (514840)     888888(4633560)    9`

So the largest is therefore D58A4, which when multiplied by 9 produces 888888.

 Posted by Charlie on 2014-09-08 11:07:11

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