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 8 eights, 8 ones (Posted on 2019-10-01)
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 No Rating

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 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)

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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