(1) You have twelve coins, one of which is known is known to be counterfeit and
therefore heavier or lighter than all the others. You also have a balance-pan
scale. In three weighings determine which coin is counterfeit and whether it
is heavier or lighter.
(2) You have ten big vats of 10-gram coins. Except that one of the vats contains
counterfeit coins, which weigh only 9 grams. You have an accurate (numerical)
scale. In one wieghing, determine which vat contains the counterfeit coins.
(3) What is the smallest number of coins this requires?
Same as above, except that any number of vats (including none) may contain
counterfeit 9-gram coins. In one weighing, find the counterfeit vats, using as
few coins as possible.
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