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8 eights, 8 ones (Posted on 2019-10-01) Difficulty: 3 of 5
The unordered set S=(1818, 8811, 1881, 1818) represents 4 distinct decimal numbers: A, B, A+B, A-B.
All "8"s denote the same digit while each "1" stands for a different digit, distinct from all the others .

What digit is not used in S ?

See The Solution Submitted by Ady TZIDON    
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Solution computer solution | Comment 1 of 2
The numbers are

3979 9948 1990 5969

so the missing digit is 2.

DefDbl A-Z
Dim crlf$, dig(9)
 

Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 
 d$ = "1234567890": h$ = d
 Do
   c = Val(Right(d, 1))
   w = 1000 * Val(Left(d, 1)) + 100 * c + 10 * Val(Mid(d, 2, 1)) + c
   x = 1100 * c + 10 * Val(Mid(d, 3, 1)) + Val(Mid(d, 4, 1))
   y = 110 * c + 1000 * Val(Mid(d, 5, 1)) + Val(Mid(d, 6, 1))
   z = 101 * c + 1000 * Val(Mid(d, 7, 1)) + 10 * Val(Mid(d, 9, 1))
   If x + y = z And Abs(x - y) = w Or x + y = w And Abs(x - y) = z Then
     Text1.Text = Text1.Text & w & Str(x) & Str(y) & Str(z) & crlf
   End If
   If x + z = w And Abs(x - z) = y Or x + z = y And Abs(x - z) = w Then
     Text1.Text = Text1.Text & w & Str(x) & Str(y) & Str(z) & crlf
   End If
   If x + w = z And Abs(x - w) = y Or x + w = y And Abs(x - w) = z Then
     Text1.Text = Text1.Text & w & Str(x) & Str(y) & Str(z) & crlf
   End If
   If w + y = z And Abs(w - y) = x Or w + y = x And Abs(w - y) = z Then
     Text1.Text = Text1.Text & w & Str(x) & Str(y) & Str(z) & crlf
   End If
   If w + z = x And Abs(w - z) = y Or w + z = y And Abs(w - z) = x Then
     Text1.Text = Text1.Text & w & Str(x) & Str(y) & Str(z) & crlf
   End If
   If z + y = x And Abs(z - y) = w Or z + y = w And Abs(z - y) = x Then
     Text1.Text = Text1.Text & w & Str(x) & Str(y) & Str(z) & crlf
   End If
   DoEvents
   permute d
 Loop Until d = h
    
    
  Text1.Text = Text1.Text & " done"
  DoEvents

End Sub

  Posted by Charlie on 2019-10-01 15:44:37
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