Have a calculation to make that should require over 1000 different calculations to find the best result. Can excel make it easier?

Heres the problem.
I have a balance or see-saw and I place 1kg at 100cm from the fulcrum and I place 2Kg 50cm from the fulcrum it would balance given force = weight*length.
Now lets give the balance 10 seperate positions and have 10 different weights.

The force calculation for the weight will change depending upon where on the balance it is placed.

I want excel to calclate the best position to have each weight to give the nearest balanced result.

I then want to be able to fix certain weights at certain positions on the balance and recalculate.

Anyone come across or had to do something similar in the past???
cheers
Nobby