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

(In reply to The answer is ... by Charlie)

I agree that if the balance can only distinguish three states, "equal" "tilts left" and "tilts right" then your logic is flawless. (A first weighing of any four against any other four reduces the pool most evenly, as there are 28 possible configurations for each of the three outcomes, but you'll still need five in the end.)

I wonder, though, if it would be in the spirit of the question to be able to distinguish with the balance that one weighing was more imbalanced than another? That is, having seen what "unequal" looks like, can you then distinguish between "unequal by the same margin", "more unequal" or "less unequal"? If so, then after your first unequal weighing you could have five outcomes not three, and you might be able to find a three-weighing scheme using that extra information.

Posted by Paul on 2005-06-24 01:38:26