How to make a "key generator" knowing the formula - vb.net

Question

I have the formula to check 9 integers,
First digit(d1) must be: 1, 2, 5, 6, 8 or 9
Last digit(d9) must be: 0 or 9
9xd1+8xd2+7xd3+6xd4+5xd5+4xd6+3xd7+2xd8+d9 mod 11 = 0
I can "validate" the key, but how can I generate more of this, knowing the conditions for it to be right?
How can I generate 9 different integers from 0 to 9 and check them under this formula?
Thanks for helping!

Answer 1

Generate the first 7 digits randomly, calculating the formula for those digits.
Set the 9th digit's value to 9, and add it to the formula.
Calculate a value for the 8th digit based on the mod of the result of the formula that causes the result of the formula to be mod 11 = 0.
For the exception case where attempting to do this causes mod 11 = 9, set the 9th digit to 0.
Implementation:
Private randGen As New Random()
Function GenNum() As Integer
Dim digits(0 To 8) As Integer
GenNum = 0
Dim checkSum As Integer
digits(0) = randGen.Next(6) + 1
If digits(0) >= 3 Then digits(0) += 2
If digits(0) >= 7 Then digits(0) += 1
checkSum += digits(0) * 9
For d As Integer = 1 To 6
digits(d) = randGen.Next(10)
checkSum += digits(d) * (9 - d)
Next
digits(8) = 9
checkSum += digits(8)
If (checkSum Mod 11) Mod 2 = 1 Then
digits(7) = (11 - (checkSum Mod 11)) \ 2
Else
digits(7) = ((12 - (checkSum Mod 11)) \ 2 + 4) Mod 10
End If
checkSum += digits(7) * 2
If checkSum Mod 11 = 9 Then digits(8) = 0
Dim pow10 As Integer = 1
For d As Integer = 8 To 0 Step -1
GenNum += pow10 * digits(d)
pow10 *= 10
Next
End Function

Answer 2

I can help you to generate integers from 0 to 9.
here is how your form should look like:
and here is the code:
Public Class Form1
Dim NumRandom As Random = New Random
Dim X, Y, Z As Integer
Private Sub GenerateBUT_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles GenerateBUT.Click
Dim a(9), i, j, RN As Integer
Dim flag As Boolean
flag = False
i = 1
a(j) = 1
Do While i <= 9
Randomize()
RN = CInt(Int(9 * Rnd()) + 1)
For j = 1 To i
If (a(j)) = RN Then
flag = True
Exit For
End If
Next
If flag = True Then
flag = False
Else
a(i) = RN
i = i + 1S
End If
Loop
Label1.Text = a(1)
Label2.Text = a(2)
Label3.Text = a(3)
Label4.Text = a(4)
Label5.Text = a(5)
Label6.Text = a(6)
Label7.Text = a(7)
Label8.Text = a(8)
Label9.Text = a(9)
Z = Label4.Text
Y = Label5.Text
X = Z + Y
X = X - Label3.Text
If X > 1 And X < 10 Then
X = NumRandom.Next(1, 7)
If X = 1 Then
Label1.Text = "0"
ElseIf X = 2 Then
Label2.Text = "0"
ElseIf X = 3 Then
Label3.Text = "0"
ElseIf X = 4 Then
Label4.Text = "0"
ElseIf X = 5 Then
Label5.Text = "0"
ElseIf X = 6 Then
Label6.Text = "0"
ElseIf X = 7 Then
Label7.Text = "0"
End If
End If
End Sub
End Class