Counterfeit Dollar |

Sally Jones has a dozen Voyageur silver dollars. However, only eleven of the coins are true silver dollars; one coin is counterfeit even though its color and size make it indistinguishable from the real silver dollars. The counterfeit coin has a different weight from the other coins but Sally does not know if it is heavier or lighter than the real coins.

Happily, Sally has a friend who loans her a very accurate balance scale.
The friend will permit
Sally three weighings to find the counterfeit coin. For instance, if
Sally weighs two coins against
each other and the scales balance then she knows these two coins are true.
Now if Sally weighs
one of the true coins against a third coin and the scales do not balance then
Sally knows the
third coin is counterfeit and she can tell whether it is light or heavy
depending on whether the
balance on which it is placed goes up or down, respectively.

By choosing her weighings carefully, Sally is able to ensure that she will
find the counterfeit coin with exactly three weighings.

1 ABCD EFGH even ABCI EFJK up ABIJ EFGH even

K is the counterfeit coin and it is light.