Another thread mentioned a problem involving 12 balls and a balance scale.

There are some interesting problems using a digital scale that provides exact weights.

The following two are theoretical problems, not practical ones. In practice, it would be better to use more weighings.

There are 15 piles of coins, 14 of which contain genuine coins, all of the same weight. The 15th pile contains counterfeit coins, all of the same weight, but different from the weight of a genuine coin. Each pile contains as many coins as you would like. You have a digital scale which provides the exact weight of any objects put on it. Using the scale three times, determine which pile contains the counterfeit coins.

Similar problem with 15 piles: 5 contain counterfeits and 10 contain true genuine coins. In three weighings determine the counterfeit and genuine piles.

The weight of neither a genuine nor a counterfeit coin is known.