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Brainteasers

Two heavy coins among five

weighinginformationcountingfake-coin

Five coins look identical. Exactly two of them are heavier than the other three, and the two heavy coins weigh the same as each other. You have a two-pan balance.

What is the smallest number of weighings that guarantees you identify both heavy coins? Explain both why fewer cannot work and how to do it.

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How many ways are there to choose which two of the five coins are heavy? Compare with the number of outcomes of two weighings.

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Balance-Scale Weighing ProblemsBalls and Bins and the Birthday ProblemBinomial Coefficients and Pascal's TriangleBurnside's Lemma and Polya CountingOptimal Card Guessing When You Count What Is Gone

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