RAY: This puzzler came to us from Clive Woods. Thanks, Clive. I think.

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. However, 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.

"The question is, how could I figure which was the pile of bogus coins in one weighing?"

TOM: If he made a weighing by taking one coin from the first pile, two from the second, three from the third...

RAY: That's exactly it!

TOM: I didn't take it further than that because I don't... what?

RAY: Count beyond three?

TOM: No-- because I don't know what I would do with the answer. But, that seemed like a good way to go about it.

RAY: That's right. You take one coin from the first pile, two from the second, three from the third, etc, all the way up to ten. That gives you 55 coins. We know that a real coin weighs ten grams, and the pile should weigh 550 grams. So, for example, if the pile weighs 548 or 552 grams, then the bogus pile is the second one and the coins either lighter by a gram or heavier by a gram. Do we have a winner?

TOM: The winner this week is Russ Bishop.

[ Car Talk Puzzler ]