Nine nickels and a traditional balance are sitting in front of you. All nickels have the same weight except for one counterfeit, which is slightly heavier than the others. What is the lowest maximum number of times you expect to use the balance to gu?

2 Answers

Oddman Profile
Oddman answered
Two (2) weighings are needed. Divide the coins into three groups of three. Compare two of them on the balance (first weighing). If they balance, the third group contains the counterfeit. Compare two coins in the heavy group (second weighing). Again, if they balance, the third coin is the counterfeit.
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Paula Schiff
Paula Schiff commented
Agreed! Although if I need to "guarantee" I'd do a 3rd weighing on the set aside coin.... But not really necessary
Oddman
Oddman commented
Only works if the odd coin is heavy (of known discrepancy).
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Ray Dart Profile
Ray Dart answered
If you take away a nickel and the remaining two groups of four balance each other, the coin you have taken away is the counterfeit. You have found it in one go. If one side is heavier than the other, that contains the counterfit. That would be your second weighing. Now split that one in two so that you have two groups of two and again you find the group that contains the counterfeit. That would be the third weighing. Now finally you split the two so that you have one coin in each side of the balance, you will find the counterfeit at the fourth weighing. So the answer is either one weighing or 4 weighings.

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