# In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However...........

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In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?

posted Oct 7, 2020

Let us make three piles (A,B,C) of 3 coins each.
1.- We have to identify the pile that contains the fake coin.
2.- We weigh A against B. Lets assume they are in balance, then pile C contains the fake coin. This is my first weighting.
3.- Then I weigh two coins of pile A against two coins of pile C . If the outcome is balance, the coin left is the fake one.
4.- In this case , I can identify the fake coin with two weightings.
5.- Going back to 3. Let´s assume the outcome is imbalance, then one of the two coins is a fake one.
6.- I weigh one coin of the pile A against one of the two coins of pile C, The outcome is balance, the other coin is the fake one . If the outcome is imbalance , the picked coin is the fake one.
Conclusion: 1 st scenario: Least number is 2
2nd scenario: Least number is 3

answer Nov 3, 2020 by anonymous

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