Simple (?) math problem

[MAYFIELDEXCEL]

You are given a random number. For this example lets use 1793
You are then given some additional numbers. For this example lets use 16, 17, & 18.

What I want to do is list out the different sets of these numbers that would equal the random number.

Some examples (Not showing them all because I don't want to have to do the math)
- ( 17 X 1 ) + ( 16 X 111 ) = 1793
- ( 17 X 97 ) + ( 18 X 8 ) = 1793

So two sets or answers would be
17x1
16x111

&

17x97
18x8

I have no idea how to do this. Any help would be greatly appreciated!

 

[KOKOSEK]

I am not sure that I am correctly understand but check something like:

Sub A()
Dim ToReach As Long
Dim X1, X2, X3 As Long
Dim x, y, z As Long
Dim counter As Long
Application.ScreenUpdating = False
counter = 10
Range("A10:C50000").ClearContents
ToReach = Range("A3").Value
X1 = Range("B3").Value
X2 = Range("C3").Value
X3 = Range("D3").Value


For x = 1 To ToReach
    For y = 1 To ToReach
        If ((X1 * y) + (X2 * x)) = ToReach Then
            Range("A" & counter).Value = "((" & X1 & "*" & y & ") + (" & X2 & "*" & x & ")) ="
            Range("C" & counter).Value = "=((" & X1 & "*" & y & ") + (" & X2 & "*" & x & "))"
            counter = counter + 1
        End If
        If ((X1 * y) + (X3 * x)) = ToReach Then
            Range("A" & counter).Value = "((" & X1 & "*" & y & ") + (" & X3 & "*" & x & ")) ="
            Range("C" & counter).Value = "=((" & X1 & "*" & y & ") + (" & X3 & "*" & x & "))"
            counter = counter + 1
        End If
        If ((X2 * y) + (X3 * x)) = ToReach Then
            Range("A" & counter).Value = "((" & X2 & "*" & y & ") + (" & X3 & "*" & x & ")) ="
            Range("C" & counter).Value = "=((" & X2 & "*" & y & ") + (" & X3 & "*" & x & "))"
            counter = counter + 1
        End If
    Next y
Next x
Application.ScreenUpdating = True
End Sub

Data in cells:
A3: number to reach
B3/C3/D3 - 3 numbers to solve

 

[MAYFIELDEXCEL]

Yeah, actually that's it exactly. Amazing!

If I wanted to add another value would I just add it like this:

Dim X1, X2, X3, X4 As Long
Dim x, y, z As Long
Dim counter As Long
Application.ScreenUpdating = False
counter = 10
Range("A10:C50000").ClearContents
ToReach = Range("A3").Value
X1 = Range("B3").Value
X2 = Range("C3").Value
X3 = Range("D3").Value
X4 = Range("E3").Value

Or would I need to add more to the if then section? Essentially If I want more than three variables?

 

[KOKOSEK]

X4 as You said.
Also add IFs with multiplying.
Now you got X1*X2 / X1*X3 / X2*X3 and you have to add X1*X4 / X2*X4 / X3*X4.