You have been given 10 bags of pearls. You are told that one of the bags is full of those cheap plastic kind of pearls, but the other nine are the real deal. Naturally, you cannot tell the difference just by looking. However, you know that the fake pearls weigh 9 grams each, while the real ones are one gram heavier and weigh 10.

Armed with a very presice scale, you could weigh a pearl from each bag until you find the fake one by weight, but that would take up to 10 weighings. Can you do it in less?

Take out one pearl per bag, making sure to remember which bag each came from. Separate into two groups of five and weigh only one group. If that group weighs 50 grams, weigh the other group. This group should weigh only 49 grams. Take off 1 pearl at a time. If you take off a real pearl, the weight will go down by 10 grams. If you remove the fake pearl, the weight will decrease by 9 grams. This method will take no more than 6 weighings.

Posted by Amanda on 2002-10-08 09:10:29