Find the lighter fake among nine coins

Question

You have nine coins that look identical. Exactly one is counterfeit and is slightly lighter than the other eight (which all weigh the same). You have a two-pan balance scale that tells you which side is heavier, lighter, or if they balance. Find the counterfeit coin using only two weighings.

Accepted Answer

The balance has three possible outcomes per weighing, so two weighings can distinguish up to 3 	imes 3 = 9 cases, exactly enough for 9 coins. Weighing 1. Split the coins into three groups of three: A, B, C. Put A on the left pan and B on the right pan. - If the pans balance, both A and B are all genuine, so the fake is in C. - If the left is lighter, the fake (being lighter) is in A. - If the right is lighter, the fake is in B. Either way, we now have three suspect coins and one weighing left. Weighing 2. Take the three suspect coins. Weigh one against another (leave the third aside). - If t…

Find the lighter fake among nine coins

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