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You are given 12 identical-looking coins, one of which is counterfeit
and weighs slightly more or less (you don't know which) than the
others.  You are given a beam balance which lets you put the same
number of coins on each side and observe which side (if either) is
heavier.  How can you identify the counterfeit and tell whether it is
heavy or light, in 3 weighings?

This puzzle was submitted in 1945 by Dwight A. Stewart, RCA, Camden, NJ to the
Graham DIAL, which circulated to over 25,000 engineers and production executives.
(cf. L. A. Graham, Ingenious Mathematical Problems and Methods, Dover, 1959, ISBN 0486205452, p. 37)

More generally, you are given N coins, one of which is heavy or light.
How many weighings do you need?  What if you only want to know which is
the counterfeit, and don't care if it is lighter or heavier?  What if
you have one coin that you know to be good?  What if you already know
that the counterfeit is lighter or heavier?  What if you are being lied
to about one of the weighing results?

[[RecPuzzlesWeighing Solution]]
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