7th All Soviet Union Mathematical Olympiad Problems 1973

7th All Soviet Union Mathematical Olympiad Problems 19731.  You are given 14 coins. It is known that genuine coins all have the same weight and that fake coins all have the same weight, but weigh less than genuine coins. You suspect that 7 particular coins are genuine and the other 7 fake. Given a balance, how can you prove this in three weighings (assuming that you

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