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No: 01       July 25, 2012


Fifty Coins

Fifty Coins

There are 50 coins. Half of them are genuine and the other half are counterfeit. Genuine coins weigh 10 grams, while counterfeit coins differ from the genuine coins by 1 gram (some of them weigh 9 grams, and some of them weigh 11 grams). You have a balance scale with two pans. In each weighing the scale shows the difference of the weights placed in each pan. You will randomly choose a coin. What is the minimum number of weighings necessary to guarantee to determine whether it is genuine or not?

Notes:

*You can't use the chosen coin in the weighing processes.
*You must place at least one coin to each pan.
*The scale displays only the difference of the weights as a non-negative number. It doesn't give any information that which side is heavier.


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