How to generate random levels for a balance game

I want to make a game like this one: http://ift.tt/1CwhmId

And I'm having troubles when trying to create the levels randomly, with an increasing difficulty.

The game consist in 1 or more balances and some objects that are placed on each side of them so that you have to determine which is the heaviest object.

There could be 1 to 4 simultaneous balances and a maximum of 2 objects per side on every balance. The amount of objects increases accordingly to the difficulty of the current level.

What i would like you to help me with is on the generation of the levels. I would like to know a good way to choose the amount of balances, the amount of objects, the weight of the objects, the amount of objects per side on the balance, and having in mind that it may happen that not every configuration leads to a 100% determinable result.

Per example, if I choose a balance and put 2 objects on each side and the sum of the weight of the objects on each side sums equal weight, the balance will not move and stay still, and it won't be possible for the user to determine which object is the heaviest.

How can I approach this problem? I'll appreciate any help that you can give me.

Thank you in advance!

Regards.