How about using a pseudo Archimedes' solution. The total correct weight of 12 lumps of gold will displace an amount of water. Tell each of the landlords that their individual 12 lumps of gold will be weighted separately, and if the displaced water is unequal from the known amount by anyone's weightings, all of the landlords will suffer some arcane, cruel, frightful torture. On the other hand, if the short changing culprit landlord confesses, pays up the shorted amount of gold, and a hefty fine, all will be forgiven. Hence, instead of one weighing, none is needed. Just an application of modern taxation policy for the average citizen? N.B: This method won't work if the landlords are politicians or big campaign donors. In which case the average citizens will have to make up the shortfall.