How many set could be formed.

[motilulla]

Hello,

Using 4 digit 0,1,2,3 in the row how many set could be formed which sum could be = 14
Note: each single digit can be used 0-to14 times too.

Like this example

0	1	2	3	Sum
14	0	0	0	14
0	4	7	3	14
1	4	5	4	14
1	6	5	2	14
2	4	7	1	14
1	8	2	3	14
1	8	4	1	14
1	7	6	0	14
3	5	5	1	14
2	6	5	1	14
1	9	3	1	14
3	4	6	1	14
2	6	4	2	14
0	14	0	0	14
0	0	14	14	14
0	0	0	14	14

<tbody>
</tbody>

Thank you all
Excel 2000
Regards,
Moti

 

[wideboydixon]

I suspect that's the 15th Tetrehedral number which would be 680. You can generate all possible sets like this:

Public Sub GenerateSets()

Const targetValue = 14

Dim nextRow As Long

Dim a As Long
Dim b As Long
Dim c As Long
Dim d As Long

nextRow = 1
For a = 0 To targetValue
    For b = 0 To targetValue - a
        For c = 0 To targetValue - a - b
            d = targetValue - a - b - c
            nextRow = nextRow + 1
            Cells(nextRow, 1) = a
            Cells(nextRow, 2) = b
            Cells(nextRow, 3) = c
            Cells(nextRow, 4) = d
        Next c
    Next b
Next a

End Sub

WBD

 

[motilulla]

I suspect that's the 15th Tetrehedral number which would be 680. You can generate all possible sets like this:

Public Sub GenerateSets()

Const targetValue = 14

Dim nextRow As Long

Dim a As Long
Dim b As Long
Dim c As Long
Dim d As Long

nextRow = 1
For a = 0 To targetValue
    For b = 0 To targetValue - a
        For c = 0 To targetValue - a - b
            d = targetValue - a - b - c
            nextRow = nextRow + 1
            Cells(nextRow, 1) = a
            Cells(nextRow, 2) = b
            Cells(nextRow, 3) = c
            Cells(nextRow, 4) = d
        Next c
    Next b
Next a

End Sub

WBD

Wow! wideboydixon,

This is perfect - thank you very much!

Regards,
Moti