Twelve Coins
17 Aug 2011

One of twelve coins is counterfeit: it is either heavier or lighter than the rest. Is it possible to identify the counterfeit coin in three weighings on a beam balance?


Classic puzzle that I first encountered in 1993-1994 time frame.


Several excellent expositions of various approaches:

  1. Solution by Brian Bundy.
  2. Solution by Jack Wert is especially pleasing.
  3. McWorter's solution.
  4. Dyson and Lyness solution.
  5. Newman's solution.
  6. Wilson's solution.

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