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Fake coins
Suppose you have five bags filled with the same type of coins and
a weigthing machine. One of this bags is completely filled with fake coins, the other bags contain only real ones. A real coin weights
10 gram and a fake one 11 gram.
What is the minimal number of times you need to use the weighting machine in order to find the bag with the fake coins?
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Solution
Take 1 coin from the first bag, 2 from the second, 3 out of the third, 4 from the fourth and 5 coins from the fifth bag. Now weigh all these coins togeheter at once. If the fake coins are in the first bag, the result of the weighting will be 11 + 20 + 30 + 40 + 50 = 151 gram. Likewise, if the fake coins are in respectively the second, the third, the fourth and the fifth bag, the result of the weighting will be 152, 153, 154 and 155 gram. Hence in this way it is possible to find the bag with the fake coins with weighting only once.
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