Need Help Running All Combinations of a Set Number of Values through 4 equations

I have 4 different equations in 4 separate cells. I am trying to test all possible value combinations from a set number to see which combination results in the smallest sum of results.

This needs to be done with combinations not permutations as order does not matter

For example...

Say I have 100 available and 4 equations as follows:

Equation 1) 2x + 5 Placed in cell A1
Equation 2) 9x^3-3x+2 Placed in cell B1
Equation 3) 3x^2-8 Placed in cell C1
Equation 4) x^4+2x Placed in cell D1

I want to run Equation 1 with x=100, Equation 2 with x=0, Equation 3 with x=0 and Equation 4 with x=0
Next, Equation 1 with x=99, Equation 2 with x=1, Equation 3 with x=0 and Equation 4 with x=0
Continuing with all possible combinations until I have Equation 1 with x=0, Equation 2 with x=0, Equation 3 with x=0 and Equation 4 with x=100.

This example has 176,851 combinations

I need to compare the sum of the results of the four equations for all iterations, and determine which iteration resulted in the smallest sum.

Is this even possible? Thank you for any help provided.

Hello shg, Thank you for your reply.

I am frequently confused by the difference between combinations and permutations, but I believe in this case, it is combinations.

If we reduced the question to say, 4 into 3 equations, the results would be as follows:

{4,0,0} -1
{3,1,0} -2
{3,0,1} -3
{2,2,0} -4
{2,1,1} -5
{2,0,2} -6
{1,3,0} -7
{1,2,1} -8
{1,1,2} -9
{1,0,3} -10
{0,4,0} -11
{0,3,1} -12
{0,2,2} -13
{0,1,3} -14
{0,0,4} -15

identical items into distinct bins... n+r-1/r-1... 4+3-1/3-1... Gives 6 choose 2

6!/2!(6-2)! = 6!/2!4! = 720/48 = 15

I believe that should be the same logic for 100 identical items into 4 distinct bins, which results in the 176,851 combinations.

Does that not seem correct?

Yes, my thoughts exactly

shg, I am in your debt. That was exactly what I needed!

Thank you so much for the time you took to whip this piece of magic up.

I'm sorry, can you tell me what I would need to do to adjust this code to work for 3 columns and 2 columns as well?

Apologies and thanks again!