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Thursday, March 18, 2010

Which stack has counterfeit coins?

Credit to this problem goes to MIT Technology Review Puzzle Corner, November/December 2009 Edition.

Given thirteen stacks each containing four coins, we are told that exactly one stack contains all counterfeit coins. A counterfeit coin weighs less than a good coin by an amount not exceeding 5 grams, and all good coins weigh an integral number of grams.

We are given a precision scale with a very wide area to put the coins on. We need to answer all these three questions all in two weighings:
1. What is the weight of a good coin?
2. What is the weight of a counterfeit coin?
3. Which stack has the counterfeit coins?

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