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BrainteasersJane StreetCitadel

Nine coins, three of them heavy

weighinginformationlower-boundcounting

Nine coins look identical. Exactly three are heavier than the rest, all by the same amount; the other six are genuine and equal. You have a two-pan balance.

  1. Show that four weighings can never guarantee identifying all three heavy coins.
  2. Is five enough?
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Count the possible sets of heavy coins and compare with the number of results four weighings can produce.

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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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