Need to generate 9 unique integers less than 100 such that no two has sum equal to another one/two numbers

Question

I need to generate 9 unique integers less than 100, such that there exists no numbers x,y and z such that x + y = z and no numbers a,b,c and d such that a + b = c + d in VB.

Here's my VB code, but it generates number sets that doesn't satisfy the latter condition.

Public Class Form1

Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
    Dim Numbers(9) As Integer
    Dim w As Integer
    Dim x As Integer
    Dim y As Integer
    Dim z As Integer
S:
    Randomize()
    Numbers(1) = CInt(Int((99 * Rnd()) + 1))
    w = 2
    Do While w < 10
        Numbers(w) = CInt(Int((99 * Rnd()) + 1))
        x = 1
        Do While x < w
            If Numbers(w) = Numbers(x) Then
                GoTo S
            End If
            x = x + 1
        Loop
        w = w + 1
    Loop
    w = 1
    x = 1
    y = 1
    Do While w < 10
        x = 1
        y = 1
        Do While x < 10
            y = 1
            Do While y < 10
                If Numbers(y) = Numbers(x) + Numbers(z) Then
                    GoTo S
                End If
                y = y + 1
            Loop
            x = x + 1
        Loop
        w = w + 1
    Loop
    w = 1
    x = 1
    y = 1
    z = 1
    Do While w < 10
        x = 1
        y = 1
        z = 1
        Do While x < 10
            y = 1
            z = 1
            Do While y < 10
                z = 1
                Do While z < 10
                    If w <> x And w <> y And w <> z And x <> y And x <> z And y <> z And Numbers(x) + Numbers(y) = Numbers(z) + Numbers(w) Then
                        GoTo S
                    End If
                    z = z + 1
                Loop
                y = y + 1
            Loop
            x = x + 1
        Loop
        w = w + 1
    Loop
    MsgBox(Numbers(1) & " " & Numbers(2) & " " & Numbers(3) & " " & Numbers(4) & " " & Numbers(5) & " " & Numbers(6) & " " & Numbers(7) & " " & Numbers(8) & " " & Numbers(9))
End Sub
End Class

What am I doing wrong?

Answer 1

Here is my suggestion.
I think you'll find it more readable:

Private Function CreateArray() As Integer()
    Dim Target As Integer()
    '' Create a list of all integers from 1 to 100, randomly sorted.
    Dim Source As List(Of Integer) = Enumerable.Range(1, 100).OrderBy(Function(orderby) Guid.NewGuid()).ToList()

    Target = New Integer(8) {}
    Dim i As Integer = 0
    For Each CurrentNumber As Integer In Source

        If ValidateNumber(CurrentNumber, Target) Then
            Target(i) = CurrentNumber
            i += 1
        End If
        If i = 9 Then
            Exit For
        End If
    Next
    Return Target

End Function

Private Function ValidateNumber(Number As Integer, Target As Integer()) As Boolean
    if Target.Length > 1 then '' otherwise there is no need to test at all
        For i As Integer = 0 To Target.Length - 3
            For j As Integer = i + 1 To Target.Length - 2
                '' First condition: the sum of any two numbers must be different than any other number
                If Target(i) + Target(j) = Number OrElse Target(i) + Number = Target(j) OrElse Target(j) + Number = Target(i) Then
                    Return False
                End If

                For k As Integer = j + 1 To Target.Length - 1
                    '' Second condition: the sum of any two numbers must be different than the sum of any other two numbers
                    If Target(i) + Target(j) = Target(k) + Number OrElse Target(i) + Target(k) = Target(k) + Number OrElse Target(i) + Number = Target(j) + Target(k) Then
                        Return False
                    End If
                Next
            Next
        Next
    end if
    Return True
End Function

You can see an example in this fiddle.

Update
I think I've found the problem in the second condition: in the second part of it I wrote Target(i) + Target(k) = Target(k) + Number, but it should have been Target(i) + Target(k) = Target(j) + Number.

I've found the problem while editing my ValidateNumber to be more readable by adding meaningful named variables for the numbers.
This is yet another reason why you should always use meaningful named variables.

Private Function ValidateNumber(Number As Integer, Target As Integer()) As Boolean
    Dim First, Second, Third As Integer
    If Target.Length > 1 Then '' otherwise there is no need to test at all
        For i As Integer = 0 To Target.Length - 3
            First = Target(i)
            For j As Integer = i + 1 To Target.Length - 2
                Second = Target(j)
                '' First condition: the sum of any two numbers must be different than any other number
                If First + Second = Number OrElse First + Number = Second OrElse Second + Number = First Then
                    Return False
                End If

                For k As Integer = j + 1 To Target.Length - 1
                    Third = Target(k)
                    '' Second condition: the sum of any two numbers must be different than the sum of any other two numbers
                    If First + Second = Third + Number OrElse First + Third = Second + Number OrElse First + Number = Second + Third Then
                        Return False
                    End If
                Next
            Next
        Next
    End If
    Return True
End Function

I've also updated the fiddle, so you can test it yourself.