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Nine times SSD (Posted on 2015-03-30) Difficulty: 3 of 5
Determine all possible positive integers N such that:
N = 9*SSD(N), where SSD(N) denotes the sum of squares of the base ten digits of N.

No Solution Yet Submitted by K Sengupta    
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Solution computer solution Comment 1 of 1
Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 
 For n = 1 To 100000
   If n / ssd(n) = 9 Then
     Text1.Text = Text1.Text & n & Str(ssd(n)) & crlf
     DoEvents
   End If
 Next n
 
 Text1.Text = Text1.Text & "done" & crlf
 
End Sub

Function ssd(x)
  tot = 0
  s$ = LTrim(Str(x))
  For i = 1 To Len(s)
    d = Val(Mid(s, i, 1))
    tot = tot + d * d
  Next
  ssd = tot
End Function

finds only

315 35

where N=315 and SSD(N) = 35.

All numbers through 5-digit length were checked. Beyond that, such an equality would be impossible as 9*(9^2)*6 is only a 4-digit number (4374).

  Posted by Charlie on 2015-03-30 22:04:20
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