"Mr.Nemo" wrote:
There are n=4 variables : x1,x2,x3,x4, each can take r=3 different
values: A,B,C. See below:
X1 A1 B1 C1
X2 A2 B2 C2
X3 A3 B3 C3
X4 A4 B4 C4
The final equation to be computed is y=x1+x2+x3+x4.
Now, there are nPr = 24 different values all the variables can assume

The number of sums is r^n (r to the power of n), not nPr.

Consider the case when n=4 and r=5; that is, x1 can have the values
a1,...,e1 for example.

The value 4P5 = PERMUT(4,5) is invalid. In fact, there are 5^4 = 625 sums.


"Mr.Nemo" wrote:
Problem Statement: Generate a macro which will list all the y values
when the values of n and r are supplied.

You also need to supply the r values for each of the n variables.

Suppose the values are in an n-by-r range of cells, and at least the
upper-left cell is selected. Also, the r+1 column must be cleared.

For example, suppose A1:E1 is 1, 2, 3, 4, 5. A2:E2 is 10,...,50. A3:E3 is
100,...,500. And A4:E4 is 1000,...,5000. This will make it easy to see
that all sums are formed. Also, clear column F.

The following macro will put all r^n sums into the r+1 column.
-----

Option Explicit

Sub allSums()
Dim x As Variant
Dim nR As Long, nC As Long, nY As Long
Dim i As Long, r As Long, c As Long
' copy matrix of values into x(nR,nC).
' assume at least 2 rows and 2 columns of values.
' assume there are no values in the nC+1 column.
x = Range(Selection(1), Selection(1).End(xlToRight).End(xlDown))
nR = UBound(x, 1)
nC = UBound(x, 2)
nY = nC ^ nR
ReDim y(0 To nY - 1, 1 To 1) As Double
For i = 0 To nY - 1
c = i
For r = 1 To nR
y(i, 1) = y(i, 1) + x(r, c Mod nC + 1)
c = c \ nC
Next
Next
Selection(1).Offset(0, nC).Resize(nY) = y
End Sub