The Counterfeit Quarters

Jun 27, 2015

RAY: This puzzler came to us from Clive Woods. Clive writes:

“I work in the Anti-Counterfeit Department of the U.S. Treasury. The other day, my assistant was sent 100 U.S. quarters, and he found that 10 of them were booooogus.

“He sorted the 10 bogus coins into one pile, and being an organized sort of chap, he made 9 piles, each containing 10 of the real coins. The weight of the counterfeit coins in this case was different from the weight of a real quarter by 1 gram. He forgot whether it was 1 gram more or 1 gram less, but, he knew that the bogus coins were all 1 gram heavier or 1 gram lighter than the real coins.

“He was called away to another job, and he left the 10 piles on his desk. I had to determine which was the bogus pile. To do it, I had a calibrated scale that would tell me the weight placed on it within a fraction of a gram. I know the weight of a real coin since I work in the what? Anti-Counterfeit Department.The question is, how could I figure which was the pile of bogus coins in one weighing?”

Ray: You take one from the first pile, two from the second, three from the third, etc. That gives you a total of 55 coins. Let’s say the genuine coins weigh 10 grams each. A pile of genuine coins should weigh 550 grams. If it weighs 548 grams, the second pile is the bogus pile, and those coins are a gram lighter. If it weighs 552 grams, it’s the second pile, and they’re heavier instead of lighter. Do we have a winner?

Tom: The winner is Russ Bishop from Punxsutawney, Pennsylvania. Congratulations!

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