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Ask Marilyn: A Classic Puzzle for Math Classes

Jake M. in Bainbridge Island, Washington, writes:

Marilyn: I'm writing because my math teacher gave us a problem that you once solved. She told us she would give extra credit to anyone who solved it in class. Well, no one did. But I took the problem home and thought about it, and I'm super stuck. So I went online to look for some hints and came across your name. Would you help me? I don't actually want the answer to the problem—just a tip to get started.

So here's the problem. "You have 15 piles of coins, each pile containing 20 coins. The coins appear to be identical in every respect; however, they're not. 14 of the piles contain coins that weight 2 grams each, but one pile is counterfeit, and those coins weigh 2.1 grams each. You have at your disposal a single pan scale, such as is used to weight produce, and your problem is to determine which of the piles contains the counterfeit coins, using the scale once and only once. You may not add or take away coins once they have been placed on the scale."

Don't tell me the answer!

Marilyn responds:

Okay, here's the way to start: Take one coin from the first pile, two coins from the second pile, three coins from the third pile, and so on, taking fifteen coins from the fifteenth pile and placing them on the scale. The rest of the answer will appear on Saturday, Dec. 8.



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