I then got an idea to try to balance the cartons on a self-made balance scale. We put the cartons on the balancescale trying to find balance. Two at a time we put them on the scale. We managed to put all the cartons on the scale without losing the balance. We then decided to remove the cartons, also two at a time and still without losing the balance. It became more difficult but we made it.
Here's what it looked like: