KöMaL 2011 A542
We have 1000 coins, but 100 of them are counterfeit. We know the weight of the real coins and it is known that the counterfeit coins are lighter than the real coins, but they may have different weights. Using a scale we want to find a counterfeit coin. Every time we can measure the total weight of a subset of the coins; the result indicates whether that set contains a counterfeit coin or not. How many measures are needed to find a counterfeit coin for sure?
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