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