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?
Label the bags "1" through "10".
Place 1 pearl from bag #1 on the scale, followed by 2 pearls from bag #2, 3 from bag #3, and so on.
Weigh the results. If all pearls were genuine, the weight would be 10! grams; the difference in grams between the result and 10! points to the bag of bogus pearls.
Solution
