You have nine brass rings, but three are actually gold. Can you pick these out using a balance scale three times at the most?

No.

There are C(9,3) = 84 possibilities as to which three of the nine are actually gold.  Three weighings, regardless of how you arrange or rearrange them, can have only 3^3 = 27 possible outcomes.  Even in the most fortuitous arrangements possible, the theoretical least number of possible weighings is Ceil(log(84)/log(3)) = 5 weighings.  (That's ceil(base-3-log(84)).

Posted by Charlie on 2005-06-23 12:56:03