We solve this problem on the basis that the balance scales give three possible results: left heavy, right heavy, equal. They don't actually work that way. The pivot is typically so sensitive that any slight imbalance will cause a left or right down situation. In order to solve the problem we have to suspend disbelief and pretend that the scales will actually balance. Maybe the bearing is a little sticky, or maybe we note that it doesn't fall very quickly - which we then interpret as a balanced state.