Populate cells based on x by y by z cell value

Question

I'm trying to populate cells based on n-1 values from three different cells. I was successful in the x by y but I'm having trouble with z

For example, I have input:

x     y     z
5     2     2

Output should be:

x should have 0, 1, 2, 3, 4; each repeated twice
y should have 0 and 1; each repeated five times
z should have 0 and 1; each repeated five times but not the same output as x or y

x   y   z
0   1   0   
1   0   0  
2   1   0  
3   0   0  
4   1   0  
0   0   0  
1   1   0  
2   0   0  
3   1   0  
4   0   0  
0   1   1  
1   0   1  
2   1   1  
3   0   1  
4   1   1  
0   0   1  
1   1   1  
2   0   1  
3   1   1  
4   0   1  

I used:

for x
=IF(ROW()<=1+A$1*A$2*A$3,INT((ROW()-2)/(A$2*A$3)),"0")

for y
=IF(ROW()<=1+A$1*A$2*A$3,MOD(ROW()-1,A$3),"0")

for z
=IF(ROW()<=1+A$1*A$2*A$3,MOD(ROW()-1,A$2),"0")

A1 to A3 has the number of items for xyz. Are there any suggestions on how I can do this?

Answer 1

Sorry for the late answer. If you let yourself use VBA (since you asked for it on your comment), let's say you have the next sheet:

You could place the next Macro on the button GO :

Sub CartesianProduct()
    'Constants:
        Dim top_x As Integer
            top_x = ActiveSheet.Cells(2, 1).Value - 1
        Dim top_y As Integer
            top_y = ActiveSheet.Cells(2, 2).Value - 1
        Dim top_z As Integer
            top_z = ActiveSheet.Cells(2, 3).Value - 1
    'Coordinates
        Dim x As Integer
        Dim y As Integer
        Dim u As Integer
    'Counter (row):
        Dim c As Integer
            c = 2
    '----------
        For x = 0 To top_x
            For y = 0 To top_y
                For z = 0 To top_z
                    ActiveSheet.Cells(c, 5).FormulaR1C1 = x
                    ActiveSheet.Cells(c, 6).FormulaR1C1 = y
                    ActiveSheet.Cells(c, 7).FormulaR1C1 = z
                    c = c + 1
                Next z
            Next y
        Next x
End Sub

Then, by clicking on GO , you fill the table with the set of the cartesian product of your sets:

If you want to avoid points with coordinates with the same value, just make the following ajust:

    For x = 0 To top_x
        For y = 0 To top_y
            For z = 0 To top_z
                If x <> y Or x <> z Or y <> z Then
                    ActiveSheet.Cells(c, 5).FormulaR1C1 = x
                    ActiveSheet.Cells(c, 6).FormulaR1C1 = y
                    ActiveSheet.Cells(c, 7).FormulaR1C1 = z
                    c = c + 1
                End If
            Next z
        Next y
    Next x