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The idea is that the counterfeit coin is lighter than the others, but not different enough to find by hand.

  • Divide the coins into 3 groups of 3. Reserve one group and put the other two groups onto the balance scale.
  • If they are the same, the counterfeit is one of the reserved group. Otherwise, the lighter pan has the counterfeit.
  • Put one coin on each side of the scale and keep one off. If they are the same, the one not weighed is the counterfeit. Otherwise it is the lighter one.
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Q: Steven has nine gold coins that are identical in appearance but one is counterfeit using a balance scale how can he find the counterfeit in just two weighings?
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