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Counterfeit CoinsA Greek trader is about to receive 20 bags, each of 100 gold coins, in payment for some goods. The trader has however received information that one of the bags contains all counterfeit coins, the distinguishing feature of the counterfeits is they weigh one gram less than a legal coin. The trader has some scales with which the exact weigh the coins and/or the bags can be determined, the trader also knows the weight of a legal coin. What is the smallest number of weighings necessary to determine which bag contains the counterfeit coins?
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