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100 coins. Some of them are fake

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You have 10 sets of ten coins. One set of the ten is counterfeit, the others are genuine. The genuine coins weigh exactly 0.10 ounces. The counterfeit coins are exactly a 0.01 ounces off, making the entire set of ten coins 0.10 ounces off. You may use an extremely accurate digital scale only once. How do you determine which set is counterfeit?

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  • Solution

Let's label the sets #0 through #9. Place 0 coins from set #0, 1 coin from set #1,  2 coins from set #2… etc… through 9 coins from set #9 on the scale, all at once. The hundredths digit on the scale display tells you which of the ten sets is counterfeit.


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