MathDB

There are

m

identical two-pan weighting scales. One of them is broken and it shows any outcome, at random. The other scales always show the correct outcome. Moreover, the weight of the broken scale differs from those of the other scales, which are all equal. At a move, we may choose a scale and place some of the other scales on its pans. Determine the greatest value of

m

for which we may find the broken scale with no more than three moves.
Proposed by A. Gribalko and O. Manzhina

Problem Statement