I hope this has an easy answer!
A batch of $n$ coins has a single fake coin, which is lighter than the rest.
The idea behind this puzzle is:
What is the largest batch of coins that can have the fake coin identified given $k$ weighings?
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$\begingroup$ Re the above comment, it's probably better to link to the source of the duplicates instead of a question which itself is a duplicate. $\endgroup$– boboquackOct 28, 2018 at 0:57
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$\begingroup$ Fun fact: Jon even commented on the linked dupe question :P $\endgroup$– QuintecOct 28, 2018 at 1:14
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1 Answer
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With this strategy
For every weighing divide the remaining coins into three equally large groups. Compare two of the groups – if one is lighter, the lighter coin is in that group, and if both have the same weight the lighter coin is in the unweighed group. Continue until the remaining group is just one coin.
We can find the fake coin in $k$ weighings
From at most $3^k$ coins.
