Sudoku - generating a puzzle

I'm a little stuck. I have a class that I'll be using to generate an entire sudoku puzzle in which right now it's almost completely working, it'll generate a board but there's always an error with it (usually 2 to 10 cells will still have a zero in it because there isn't an available number to be filled in)

Currently here's what I'm doing: I have a 9x9 array of type Integer and I have a 9x9 array of type List(Of Integer) and each element in the list array has the numbers 1 through 9. To fill the 9x9 Integer array I simply start with position 0,0 and work to 8,8 randomly picking a number from the List then a sub will go through and remove that number from the current column, the current row and the current mini-grid.

This is why there's random cells that still have a 0 (zero) in them, it's because there isn't a number available for that cell because of the cells that came before it and this is where I'm stuck.

Here's the code:

Code:

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Option Explicit On
Option Strict On

Friend Class SudokuBoard

    Private WithEvents bw As New System.ComponentModel.BackgroundWorker
    Private m_TheBoard(8I, 8I) As Integer
    Private m_Numbers(8, 8) As List(Of Integer)

    Friend Event BoardGenerated(ByVal TheBoard(,) As Integer)

#Region " Constructors "
    Friend Sub New()
        Me.GenerateBoard()
    End Sub
#End Region
#Region " GenerateBoard "
    Friend Sub GenerateBoard()
        Call Me.ClearBoard()
        Me.bw.RunWorkerAsync()
    End Sub

    Private Sub bw_DoWork(ByVal sender As Object, ByVal e As System.ComponentModel.DoWorkEventArgs) Handles bw.DoWork
        Dim Rand As New Random
        'Dim Index As Integer

        For x As Integer = 0I To 8I
            For y As Integer = 0I To 8I
                m_Numbers(x, y) = New List(Of Integer)
                m_Numbers(x, y).AddRange(New Integer() {1, 2, 3, 4, 5, 6, 7, 8, 9})
            Next y
        Next x

        For x As Integer = 0I To 8I
            For y As Integer = 0I To 8I
                Select Case m_Numbers(x, y).Count
                    Case 0
                        'No available numbers
                    Case 1
                        'Try
                        m_TheBoard(x, y) = m_Numbers(x, y)(0I)
                        'Catch
                        'End Try
                    Case Is > 1
                        'Try
                        'Index = Rand.Next(0I, m_Numbers(x, y).Count)
                        m_TheBoard(x, y) = m_Numbers(x, y)(Rand.Next(0I, m_Numbers(x, y).Count))
                        'Catch
                        'End Try
                End Select
                RemoveUsedValue(x, y)
            Next y
        Next x
    End Sub

    Private Sub bw_RunWorkerCompleted(ByVal sender As Object, ByVal e As System.ComponentModel.RunWorkerCompletedEventArgs) Handles bw.RunWorkerCompleted
        Dim Copy(8, 8) As Integer
        For x As Integer = 0I To 8I
            For y As Integer = 0I To 8I
                Copy(x, y) = m_TheBoard(x, y)
            Next y
        Next x
        RaiseEvent BoardGenerated(Copy)
    End Sub
#End Region
#Region " Friend Methods "
    Friend Sub ClearBoard()
        For x As Integer = 0I To 8I
            For y As Integer = 0I To 8I
                Me.SetNumber(x, y)
            Next y
        Next x
    End Sub

    Friend Sub SetNumber(ByVal Row As Integer, ByVal Col As Integer)
        m_TheBoard(Row, Col) = 0I
    End Sub
#End Region
#Region " RemoveUsedValue "
    Private Sub RemoveUsedValue(ByVal Row As Integer, ByVal Col As Integer)
        Dim CurrNumber As Integer = m_TheBoard(Row, Col)
        For i As Integer = 0I To 8I
            m_Numbers(Row, i).Remove(CurrNumber)
        Next i
        For i As Integer = 0I To 8I
            m_Numbers(i, Col).Remove(CurrNumber)
        Next i
        Select Case Get3x3(Row, Col)
            Case "A1"
                'A1, A2, A3
                'B1, B2, B3
                'C1, C2, C3
                m_Numbers(0, 0).Remove(CurrNumber)
                m_Numbers(0, 1).Remove(CurrNumber)
                m_Numbers(0, 2).Remove(CurrNumber)
                m_Numbers(1, 0).Remove(CurrNumber)
                m_Numbers(1, 1).Remove(CurrNumber)
                m_Numbers(1, 2).Remove(CurrNumber)
                m_Numbers(2, 0).Remove(CurrNumber)
                m_Numbers(2, 1).Remove(CurrNumber)
                m_Numbers(2, 2).Remove(CurrNumber)
            Case "A2"
                'A4, A5, A6
                'B4, B5, B6
                'C4, C5, C6
                m_Numbers(0, 3).Remove(CurrNumber)
                m_Numbers(0, 4).Remove(CurrNumber)
                m_Numbers(0, 5).Remove(CurrNumber)
                m_Numbers(1, 3).Remove(CurrNumber)
                m_Numbers(1, 4).Remove(CurrNumber)
                m_Numbers(1, 5).Remove(CurrNumber)
                m_Numbers(2, 3).Remove(CurrNumber)
                m_Numbers(2, 4).Remove(CurrNumber)
                m_Numbers(2, 5).Remove(CurrNumber)
            Case "A3"
                'A7, A8, A9
                'B7, B8, B9
                'C7, C8, C9
                m_Numbers(0, 6).Remove(CurrNumber)
                m_Numbers(0, 7).Remove(CurrNumber)
                m_Numbers(0, 8).Remove(CurrNumber)
                m_Numbers(1, 6).Remove(CurrNumber)
                m_Numbers(1, 7).Remove(CurrNumber)
                m_Numbers(1, 8).Remove(CurrNumber)
                m_Numbers(2, 6).Remove(CurrNumber)
                m_Numbers(2, 7).Remove(CurrNumber)
                m_Numbers(2, 8).Remove(CurrNumber)
            Case "B1"
                'D1, D2, D3
                'E1, E2, E3
                'F1, F2, F3
                m_Numbers(3, 0).Remove(CurrNumber)
                m_Numbers(3, 1).Remove(CurrNumber)
                m_Numbers(3, 2).Remove(CurrNumber)
                m_Numbers(4, 0).Remove(CurrNumber)
                m_Numbers(4, 1).Remove(CurrNumber)
                m_Numbers(4, 2).Remove(CurrNumber)
                m_Numbers(5, 0).Remove(CurrNumber)
                m_Numbers(5, 1).Remove(CurrNumber)
                m_Numbers(5, 2).Remove(CurrNumber)
            Case "B2"
                'D4, D5, D6
                'E4, E5, E6
                'F4, F5, F6
                m_Numbers(3, 3).Remove(CurrNumber)
                m_Numbers(3, 4).Remove(CurrNumber)
                m_Numbers(3, 5).Remove(CurrNumber)
                m_Numbers(4, 3).Remove(CurrNumber)
                m_Numbers(4, 4).Remove(CurrNumber)
                m_Numbers(4, 5).Remove(CurrNumber)
                m_Numbers(5, 3).Remove(CurrNumber)
                m_Numbers(5, 4).Remove(CurrNumber)
                m_Numbers(5, 5).Remove(CurrNumber)
            Case "B3"
                'D7, D8, D9
                'E7, E8, E9
                'F7, F8, F9
                m_Numbers(3, 6).Remove(CurrNumber)
                m_Numbers(3, 7).Remove(CurrNumber)
                m_Numbers(3, 8).Remove(CurrNumber)
                m_Numbers(4, 6).Remove(CurrNumber)
                m_Numbers(4, 7).Remove(CurrNumber)
                m_Numbers(4, 8).Remove(CurrNumber)
                m_Numbers(5, 6).Remove(CurrNumber)
                m_Numbers(5, 7).Remove(CurrNumber)
                m_Numbers(5, 8).Remove(CurrNumber)
            Case "C1"
                'G1, G2, G3
                'H1, H2, H3
                'I1, I2, I3
                m_Numbers(6, 0).Remove(CurrNumber)
                m_Numbers(6, 1).Remove(CurrNumber)
                m_Numbers(6, 2).Remove(CurrNumber)
                m_Numbers(7, 0).Remove(CurrNumber)
                m_Numbers(7, 1).Remove(CurrNumber)
                m_Numbers(7, 2).Remove(CurrNumber)
                m_Numbers(8, 0).Remove(CurrNumber)
                m_Numbers(8, 1).Remove(CurrNumber)
                m_Numbers(8, 2).Remove(CurrNumber)
            Case "C2"
                'G4, G5, G6
                'H4, H5, H6
                'I4, I5, I6
                m_Numbers(6, 3).Remove(CurrNumber)
                m_Numbers(6, 4).Remove(CurrNumber)
                m_Numbers(6, 5).Remove(CurrNumber)
                m_Numbers(7, 3).Remove(CurrNumber)
                m_Numbers(7, 4).Remove(CurrNumber)
                m_Numbers(7, 5).Remove(CurrNumber)
                m_Numbers(8, 3).Remove(CurrNumber)
                m_Numbers(8, 4).Remove(CurrNumber)
                m_Numbers(8, 5).Remove(CurrNumber)
            Case "C3"
                'G7, G8, G9
                'h7, H8, H9
                'I7, I8, I9
                m_Numbers(6, 6).Remove(CurrNumber)
                m_Numbers(6, 7).Remove(CurrNumber)
                m_Numbers(6, 8).Remove(CurrNumber)
                m_Numbers(7, 6).Remove(CurrNumber)
                m_Numbers(7, 7).Remove(CurrNumber)
                m_Numbers(7, 8).Remove(CurrNumber)
                m_Numbers(8, 6).Remove(CurrNumber)
                m_Numbers(8, 7).Remove(CurrNumber)
                m_Numbers(8, 8).Remove(CurrNumber)
        End Select
    End Sub
#End Region
#Region " Get3x3 "
    Private Function Get3x3(ByVal x As Integer, ByVal y As Integer) As String
        Dim X_Val As Char, Y_Val As Integer
        Select Case x
            Case 0, 1, 2 : X_Val = "A"c
            Case 3, 4, 5 : X_Val = "B"c
            Case 6, 7, 8 : X_Val = "C"c
        End Select
        Select Case y
            Case 0, 1, 2 : Y_Val = 1
            Case 3, 4, 5 : Y_Val = 2
            Case 6, 7, 8 : Y_Val = 3
        End Select
        Return X_Val & Y_Val
    End Function
#End Region
End Class

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Do you read C#, This guy seems to have it down.

http://www.c-sharpcorner.com/UploadF...5-a812535c45e5

With some help it's working correctly now, here's the code:
http://www.vbforums.com/showthread.php?p=3249653